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It connects angles to coordinates and provides a visual, intuitive way to understand ",e.jsx("strong",{children:"sine"}),", ",e.jsx("strong",{children:"cosine"}),", and ",e.jsx("strong",{children:"tangent"})," for any angle."]}),e.jsx("p",{className:"text-lg text-muted-foreground",children:"This guide covers special angles, radian-degree conversion, coordinates on the circle, reference angles, memory tricks, worked examples with full steps, and an interactive unit circle explorer."})]}),e.jsxs("nav",{className:"mb-12 rounded-xl border border-border bg-muted/30 p-6 lg:hidden",children:[e.jsx("h2",{className:"text-sm font-semibold uppercase tracking-wider text-muted-foreground mb-3",children:"In this guide"}),e.jsx("ol",{className:"space-y-1.5 text-sm",children:Q.map(l=>e.jsx("li",{children:e.jsx("a",{href:`#${l.id}`,className:"text-primary hover:underline",children:l.label})},l.id))})]}),e.jsxs("section",{id:"introduction",className:"mb-14 scroll-mt-20",children:[e.jsx("a",{href:"#introduction",className:"group no-underline",children:e.jsxs("h2",{className:"text-2xl font-bold mb-4 flex items-center gap-2",children:[e.jsx("span",{className:"flex items-center justify-center w-8 h-8 rounded-full bg-primary text-white text-sm font-bold",children:"1"}),"Introduction",e.jsx(h,{className:"h-4 w-4 text-muted-foreground opacity-0 group-hover:opacity-100 transition-opacity"})]})}),e.jsx("p",{className:"text-muted-foreground mb-3",children:"The Unit Circle is a cornerstone of trigonometry. Itâs a simple c
6oncept with far-reaching implications, connecting angles, coordinates, and trigonometric functions in a beautifully elegant way."}),e.jsxs("p",{className:"text-muted-foreground mb-4",children:["Simply put, the Unit Circle is a circle centered at the ",e.jsx("strong",{children:"origin (0, 0)"})," of a coordinate plane with a ",e.jsx("strong",{children:"radius of exactly 1 unit"}),". Its equation is ",e.jsx("strong",{children:"x² + y² = 1"}),"."]}),e.jsxs("div",{className:"rounded-xl border border-primary/20 bg-gradient-to-br from-primary/5 to-primary/10 p-5 mb-6",children:[e.jsxs("div",{className:"flex items-center gap-2 mb-2",children:[e.jsx(ie,{className:"h-4 w-4 text-primary flex-shrink-0"}),e.jsx("span",{className:"text-xs font-bold uppercase tracking-widest text-primary",children:"Picture This"})]}),e.jsx("p",{className:"text-lg italic font-serif text-foreground leading-relaxed",children:"Imagine standing at the center of a clock. The hands sweep out angles. Now, imagine that clock face is perfectly sized so that its hands are exactly 1 unit long. As a hand sweeps around, its tip traces out the Unit Circle. The position of that tip (its x and y coordinates) tells us the cosine and sine of the angle."})]}),e.jsxs("div",{className:"rounded-xl border border-amber-200 bg-gradient-to-br from-amber-50 to-amber-100/60 p-5",children:[e.jsxs("div",{className:"flex items-center gap-2 mb-2",children:[e.jsx(F,{className:"h-4 w-4 text-amber-600 flex-shrink-0"}),e.jsx("span",{className:"text-xs font-bold uppercase tracking-widest text-amber-700",children:"Why It Matters"})]}),e.jsxs("p",{className:"text-sm text-amber-900",children:["The unit circle is crucial for ",e.jsx("strong",{children:"pre-calculus"}),", ",e.jsx("strong",{children:"calculus"}),", ",e.jsx("strong",{children:"physics"}),", and ",e.jsx("strong",{children:"engineering"}),", where understanding periodic functions and circular motion is key. It defines trig functions for ",e.jsx("em",{children:"any"})," angle, not just those in right triangles."]})]})]}),e.jsxs("section",{id:"key-definitions",className:"mb-14 scroll-mt-20",children:[e.jsx("a",{href:"#key-definitions",className:"group no-underline",children:e.jsxs("h2",{className:"text-2xl font-bold mb-4 flex items-center gap-2",children:[e.jsx("span",{className:"flex items-center justify-center w-8 h-8 rounded-full bg-primary text-white text-sm font-bold",children:"2"}),"Key Definitions",e.jsx(h,{className:"h-4 w-4 text-muted-foreground opacity-0 group-hover:opacity-100 transition-opacity"})]})}),e.jsxs("div",{className:"grid sm:grid-cols-2 gap-3 mb-4",children:[e.jsxs("div",{className:"rounded-lg border border-border bg-muted/30 p-4",children:[e.jsx("p",{className:"text-sm font-bold text-foreground",children:"Unit Circle"}),e.jsx("p",{className:"text-xs text-muted-foreground mt-1",children:"A circle with radius 1, centered at the origin (0,0). Equation: x² + y² = 1."})]}),e.jsxs("div",{className:"rounded-lg border border-border bg-muted/30 p-4",children:[e.jsx("p",{className:"text-sm font-bold text-foreground",children:"Radian"}),e.jsx("p",{className:"text-xs text-muted-foreground mt-1",children:"An angle unit where the arc length equals the radius. 2Ï radians = 360°."})]}),e.jsxs("div",{className:"rounded-lg border border-border bg-muted/30 p-4",children:[e.jsxs("p",{className:"text-sm font-bold text-foreground",children:["Reference Angle (θ",e.jsx("sub",{children:"R"}),")"]}),e.jsx("p",{className:"text-xs text-muted-foreground mt-1",children:"The acute angle formed by the terminal side and the x-axis. Always between 0° and 90°."})]}),e.jsxs("div",{className:"rounded-lg border border-border bg-muted/30 p-4",children:[e.jsx("p",{className:"text-sm font-bold text-foreground",children:"Terminal Side"}),e.jsx("p",{className:"text-xs text-muted-foreground mt-1",children:"The ray that rotates around the origin to form an angle. Starts at the positive x-axis."})]}),e.jsxs("div",{className:"rounded-lg border border-border bg-muted/30 p-4",children:[e.jsx("p",{className:"text-sm font-bold text-foreground",children:"Cosine (cos θ)"}),e.jsxs("p",{className:"text-xs text-muted-foreground mt-1",children:["The ",e.jsx("strong",{children:"x-coordinate"})," of the point where the terminal side intersects the unit circle."]})]}),e.jsxs("div",{className:"rounded-lg border border-border bg-muted/30 p-4",children:[e.jsx("p",{className:"text-sm font-bold text-foreground",children:"Sine (sin θ)"}),e.jsxs("p",{className:"text-xs text-muted-foreground mt-1",children:["The ",e.jsx("strong",{children:"y-coordinate"})," of the point where the terminal side intersects the unit circle."]})]}),e.jsxs("div",{className:"rounded-lg border border-border bg-muted/30 p-4",children:[e.jsx("p",{className:"text-sm font-bold text-foreground",children:"Tangent (tan θ)"}),e.jsx("p",{className:"text-xs text-muted-foreground mt-1",children:"The ratio sinθ/cosθ = y/x. Undefined when cosθ = 0."})]}),e.jsxs("div",{className:"rounded-lg border border-border bg-muted/30 p-4",children:[e.jsx("p",{className:"text-sm font-bold text-foreground",children:"Quadrants"}),e.jsx("p",{className:"text-xs text-muted-foreground mt-1",children:"Four regions of the coordinate plane, numbered IâIV counter-clockwise from the top-right."})]})]}),e.jsxs("div",{className:"grid grid-cols-2 gap-3 mb-4",children:[e.jsxs("div",{className:"rounded-xl border-2 border-green-200 bg-gradient-to-br from-green-50 to-green-100/50 p-4 text-center",children:[e.jsx("p",{className:"text-sm font-bold text-green-800 mb-1",children:"Quadrant I (0°â90°)"}),e.jsx("p",{className:"text-xs text-green-700",children:"x > 0, y > 0"}),e.jsx("p",{className:"text-[10px] text-green-600 mt-1",children:"sin +, cos +, tan +"})]}),e.jsxs("div",{className:"rounded-xl border-2 border-blue-200 bg-gradient-to-br from-blue-50 to-blue-100/50 p-4 text-center",children:[e.jsx("p",{className:"text-sm font-bold text-blue-800 mb-1",children:"Quadrant II (90°â180°)"}),e.jsx("p",{className:"text-xs text-blue-700",children:"x < 0, y > 0"}),e.jsx("p",{className:"text-[10px] text-blue-600 mt-1",children:"sin +, cos â, tan â"})]}),e.jsxs("div",{className:"rounded-xl border-2 border-amber-200 bg-gradient-to-br from-amber-50 to-amber-100/50 p-4 text-center",children:[e.jsx("p",{className:"text-sm font-bold text-amber-800 mb-1",children:"Quadrant III (180°â270°)"}),e.jsx("p",{className:"text-xs text-amber-700",children:"x < 0, y < 0"}),e.jsx("p",{className:"text-[10px] text-amber-600 mt-1",children:"sin â, cos â, tan +"})]}),e.jsxs("div",{className:"rounded-xl border-2 border-violet-200 bg-gradient-to-br from-violet-50 to-violet-100/50 p-4 text-center",children:[e.jsx("p",{className:"text-sm font-bold text-violet-800 mb-1",children:"Quadrant IV (270°â360°)"}),e.jsx("p",{className:"text-xs text-violet-700",children:"x > 0, y < 0"}),e.jsx("p",{className:"text-[10px] text-violet-600 mt-1",children:"sin â, cos +, tan â"})]})]}),e.jsxs("div",{className:"rounded-xl border border-amber-200 bg-gradient-to-br from-amber-50 to-amber-100/60 p-5",children:[e.jsxs("div",{className:"flex items-center gap-2 mb-2",children:[e.jsx(F,{className:"h-4 w-4 text-amber-600 flex-shrink-0"}),e.jsx("span",{className:"text-xs font-bold uppercase tracking-widest text-amber-700",children:"Important"})]}),e.jsxs("p",{className:"text-sm text-amber-900",children:["Any point on the unit circle can be written as ",e.jsx("strong",{children:"(cos θ, sin θ)"}),". The x-coordinate is always cosine and the y-coordinate is always sine. This is the foundation of the unit circle."]})]})]}),e.jsxs("section",{id:"radian-degree",className:"mb-14 scroll-mt-20",children:[e.jsx("a",{href:"#radian-degree",className:"group no-underline",children:e.jsxs("h2",{className:"text-2xl font-bold mb-4 flex items-center gap-2",children:[e.jsx("span",{className:"flex items-center justify-center w-8 h-8 rounded-full bg-primary text-white text-sm font-bold",children:"3"}),"Radian vs Degree Conversion",e.jsx(h,{className:"h-4 w-4 text-muted-foreground opacity-0 group-hover:opacity-100 transition-opacity"})]})}),e.jsxs("p",{className:"text-muted-foreground mb-4",children:["Angles can be measured in degrees or radians. The key relationship is ",e.jsx("strong",{children:"180° = Ï radians"}),"."]}),e.jsxs("div",{className:"grid sm:grid-cols-2 gap-3 mb-6",children:[e.jsxs("div",{className:"rounded-xl border-2 border-blue-200 bg-gradient-to-br from-blue-50 to-blue-100/50 p-5",children:[e.jsx("p",{className:"text-sm font-bold text-blue-800 mb-2",children:"Degrees â Radians"}),e.jsx("p",{className:"text-center font-mono text-sm text-blue-700 mb-2",children:"Radians = Degrees à Ï/180°"}),e.jsxs("div",{className:"border-t border-blue-200 pt-2 text-xs text-blue-600 space-y-0.5",children:[e.jsx("p",{children:"60° à Ï/180 = Ï/3"}),e.jsx("p",{children:"90° à Ï/180 = Ï/2"}),e.jsx("p",{children:"45° à Ï/180 = Ï/4"})]})]}),e.jsxs("div",{className:"rounded-xl border-2 border-green-200 bg-gradient-to-br from-green-50 to-green-100/50 p-5",children:[e.jsx("p",{className:"text-sm font-bold text-green-800 mb-2",children:"Radians â Degrees"}),e.jsx("p",{className:"text-center font-mono text-sm text-green-700 mb-2",children:"Degrees = Radians à 180°/Ï"}),e.jsxs("div",{className:"border-t border-green-200 pt-2 text-xs text-green-600 space-y-0.5",children:[e.jsx("p",{children:"Ï/6 à 180/Ï = 30°"}),e.jsx("p",{children:"Ï/4 à 180/Ï = 45°"}),e.jsx("p",{children:"2Ï/3 à 180/Ï = 120°"})]})]})]}),e.jsx("h3",{className:"text-xl font-semibold mb-3",children:"Common Conversions"}),e.jsx("div",{className:"overflow-x-auto mb-4",children:e.jsxs("table",{className:"w-full text-sm border border-border rounded-lg overflow-hidden",children:[e.jsx("thead",{children:e.jsxs("tr",{className:"bg-muted/50",children:[e.jsx("th",{className:"px-4 py-2 text-left font-semibold text-foreground border-b border-border",children:"Degrees"}),e.jsx("th",{className:"px-4 py-2 text-center font-semibold text-foreground border-b border-border",children:"Radians"})]})}),e.jsxs("tbody",{className:"font-mono text-center",children:[e.jsxs("tr",{className:"border-b border-border",children:[e.jsx("td",{className:"px-4 py-2 font-sans text-left",children:"0°"}),e.jsx("td",{className:"px-4 py-2",children:"0"})]}),e.jsxs("tr",{className:"border-b border-border bg-muted/20",children:[e.jsx("td",{className:"px-4 py-2 font-sans text-left",children:"30°"}),e.jsx("td",{className:"px-4 py-2",children:"Ï/6"})]}),e.jsxs("tr",{className:"border-b border-border",children:[e.jsx("td",{className:"px-4 py-2 font-sans text-left",children:"45°"}),e.jsx("td",{className:"px-4 py-2",children:"Ï/4"})]}),e.jsxs("tr",{className:"border-b border-border bg-muted/20",children:[e.jsx("td",{className:"px-4 py-2 font-sans text-left",children:"60°"}),e.jsx("td",{className:"px-4 py-2",children:"Ï/3"})]}),e.jsxs("tr",{className:"border-b border-border",children:[e.jsx("td",{className:"px-4 py-2 font-sans text-left",children:"90°"}),e.jsx("td",{className:"px-4 py-2",children:"Ï/2"})]}),e.jsxs("tr",{className:"border-b border-border bg-muted/20",children:[e.jsx("td",{className:"px-4 py-2 font-sans text-left",children:"120°"}),e.jsx("td",{className:"px-4 py-2",children:"2Ï/3"})]}),e.jsxs("tr",{className:"border-b border-border",children:[e.jsx("td",{className:"px-4 py-2 font-sans text-left",children:"180°"}),e.jsx("td",{className:"px-4 py-2",children:"Ï"})]}),e.jsxs("tr",{className:"border-b border-border bg-muted/20",children:[e.jsx("td",{className:"px-4 py-2 font-sans text-left",children:"270°"}),e.jsx("td",{className:"px-4 py-2",children:"3Ï/2"})]}),e.jsxs("tr",{children:[e.jsx("td",{className:"px-4 py-2 font-sans text-left",children:"360°"}),e.jsx("td",{className:"px-4 py-2",children:"2Ï"})]})]})]})})]}),e.jsxs("section",{id:"coordinates",className:"mb-14 scroll-mt-20",children:[e.jsx("a",{href:"#coordinates",className:"group no-underline",children:e.jsxs("h2",{className:"text-2xl font-bold mb-4 flex items-center gap-2",children:[e.jsx("span",{className:"flex items-center justify-center w-8 h-8 rounded-full bg-primary text-white text-sm font-bold",children:"4"}),"Coordinates on the Unit Circle",e.jsx(h,{className:"h-4 w-4 text-muted-foreground opacity-0 group-hover:opacity-100 transition-opacity"})]})}),e.jsx("p",{className:"text-muted-foreground mb-4",children:"For any angle θ in standard position, the point where its terminal side intersects the unit circle has special significance:"}),e.jsxs("div",{className:"rounded-xl border-2 border-primary/20 bg-gradient-to-br from-primary/5 to-primary/10 p-5 mb-6 text-center",children:[e.jsx("p",{className:"text-lg font-bold text-foreground mb-2",children:"P(x, y) = (cos θ, sin θ)"}),e.jsxs("div",{className:"grid grid-cols-3 gap-3 mt-3",children:[e.jsxs("div",{children:[e.jsx("p",{className:"text-xs font-semibold text-blue-600 uppercase",children:"x-coordinate"}),e.jsx("p",{className:"text-sm font-bold text-foreground",children:"cos θ"})]}),e.jsxs("div",{children:[e.jsx("p",{className:"text-xs font-semibold text-red-600 uppercase",children:"y-coordinate"}),e.jsx("p",{className:"text-sm font-bold text-foreground",children:"sin θ"})]}),e.jsxs("div",{children:[e.jsx("p",{className:"text-xs font-semibold text-amber-600 uppercase",children:"tangent"}),e.jsx("p",{className:"text-sm font-bold text-foreground",children:"sin θ / cos θ"})]})]})]}),e.jsxs("p",{className:"text-muted-foreground mb-4",children:["This is why tan θ is ",e.jsx("strong",{children:"undefined"})," when cos θ = 0 (at 90° and 270°) â you cannot divide by zero."]}),e.jsx(ce,{})]}),e.jsxs("section",{id:"special-angles",className:"mb-14 scroll-mt-20",children:[e.jsx("a",{href:"#special-angles",className:"group no-underline",children:e.jsxs("h2",{className:"text-2xl font-bold mb-4 flex items-center gap-2",children:[e.jsx("span",{className:"flex items-center justify-center w-8 h-8 rounded-full bg-primary text-white text-sm font-bold",children:"5"}),"Special Angles",e.jsx(h,{className:"h-4 w-4 text-muted-foreground opacity-0 group-hover:opacity-100 transition-opacity"})]})}),e.jsx("p",{className:"text-muted-foreground mb-4",children:"There are certain âspecialâ angles on the unit circle that you should memorize. Here are the key angles in the first quadrant:"}),e.jsx("div",{className:"overflow-x-auto mb-6",children:e.jsxs("table",{className:"w-full text-sm border border-border rounded-lg overflow-hidden",children:[e.jsx("thead",{children:e.jsxs("tr",{className:"bg-muted/50",children:[e.jsx("th",{className:"px-4 py-2 text-left font-semibold text-foreground border-b border-border",children:"Degrees"}),e.jsx("th",{className:"px-4 py-2 text-center font-semibold text-foreground border-b border-border",children:"Radians"}),e.jsx("th",{className:"px-4 py-2 text-center font-semibold text-blue-600 border-b border-border",children:"cos θ (x)"}),e.jsx("th",{className:"px-4 py-2 text-center font-semibold text-red-600 border-b border-border",children:"sin θ (y)"}),e.jsx("th",{className:"px-4 py-2 text-center font-semibold text-amber-600 border-b border-border",children:"tan θ"})]})}),e.jsxs("tbody",{className:"font-mono",children:[e.jsxs("tr",{className:"border-b border-border",children:[e.jsx("td",{className:"px-4 py-2 font-sans font-medium",children:"0°"}),e.jsx("td",{className:"px-4 py-2 text-center",children:"0"}),e.jsx("td",{className:"px-4 py-2 text-center",children:"1"}),e.jsx("td",{className:"px-4 py-2 text-center",children:"0"}),e.jsx("td",{className:"px-4 py-2 text-center",children:"0"})]}),e.jsxs("tr",{className:"border-b border-border bg-muted/20",children:[e.jsx("td",{className:"px-4 py-2 font-sans font-medium",children:"30°"}),e.jsx("td",{className:"px-4 py-2 text-center",children:"Ï/6"}),e.jsx("td",{className:"px-4 py-2 text-center",children:"â3/2"}),e.jsx("td",{className:"px-4 py-2 text-center",children:"1/2"}),e.jsx("td",{className:"px-4 py-2 text-center",children:"â3/3"})]}),e.jsxs("tr",{className:"border-b border-border",children:[e.jsx("td",{className:"px-4 py-2 font-sans font-medium",children:"45°"}),e.jsx("td",{className:"px-4 py-2 text-center",children:"Ï/4"}),e.jsx("td",{className:"px-4 py-2 text-center",children:"â2/2"}),e.jsx("td",{className:"px-4 py-2 text-center",children:"â2/2"}),e.jsx("td",{className:"
6px-4 py-2 text-center",children:"1"})]}),e.jsxs("tr",{className:"border-b border-border bg-muted/20",children:[e.jsx("td",{className:"px-4 py-2 font-sans font-medium",children:"60°"}),e.jsx("td",{className:"px-4 py-2 text-center",children:"Ï/3"}),e.jsx("td",{className:"px-4 py-2 text-center",children:"1/2"}),e.jsx("td",{className:"px-4 py-2 text-center",children:"â3/2"}),e.jsx("td",{className:"px-4 py-2 text-center",children:"â3"})]}),e.jsxs("tr",{children:[e.jsx("td",{className:"px-4 py-2 font-sans font-medium",children:"90°"}),e.jsx("td",{className:"px-4 py-2 text-center",children:"Ï/2"}),e.jsx("td",{className:"px-4 py-2 text-center",children:"0"}),e.jsx("td",{className:"px-4 py-2 text-center",children:"1"}),e.jsx("td",{className:"px-4 py-2 text-center",children:"undef"})]})]})]})}),e.jsxs("div",{className:"rounded-xl border border-amber-200 bg-gradient-to-br from-amber-50 to-amber-100/60 p-5",children:[e.jsxs("div",{className:"flex items-center gap-2 mb-2",children:[e.jsx(F,{className:"h-4 w-4 text-amber-600 flex-shrink-0"}),e.jsx("span",{className:"text-xs font-bold uppercase tracking-widest text-amber-700",children:"Important"})]}),e.jsxs("p",{className:"text-sm text-amber-900",children:["Coordinates for angles in other quadrants are derived from these first-quadrant values using ",e.jsx("strong",{children:"reference angles"})," and ",e.jsx("strong",{children:"quadrant signs"}),". The magnitudes are the same â only the signs change."]})]})]}),e.jsxs("section",{id:"memory-trick",className:"mb-14 scroll-mt-20",children:[e.jsx("a",{href:"#memory-trick",className:"group no-underline",children:e.jsxs("h2",{className:"text-2xl font-bold mb-4 flex items-center gap-2",children:[e.jsx("span",{className:"flex items-center justify-center w-8 h-8 rounded-full bg-primary text-white text-sm font-bold",children:"6"}),"The âAll Over 2â Memory Trick",e.jsx(h,{className:"h-4 w-4 text-muted-foreground opacity-0 group-hover:opacity-100 transition-opacity"})]})}),e.jsxs("p",{className:"text-muted-foreground mb-4",children:["Instead of memorizing each coordinate separately, notice that every special angle value follows a pattern of ",e.jsx("strong",{children:"ân / 2"}),"."]}),e.jsxs("div",{className:"rounded-xl border-2 border-violet-200 bg-gradient-to-br from-violet-50 to-violet-100/50 p-5 mb-6",children:[e.jsx("p",{className:"text-sm font-bold text-violet-800 mb-3",children:"For Sine (y-values) â count UP from 0:"}),e.jsxs("div",{className:"grid grid-cols-5 gap-2 text-center font-mono text-sm mb-4",children:[e.jsxs("div",{className:"rounded-lg bg-white/70 p-2",children:[e.jsx("p",{className:"text-xs text-muted-foreground",children:"0°"}),e.jsx("p",{className:"text-violet-700",children:"â0/2"}),e.jsx("p",{className:"text-xs font-bold text-foreground mt-1",children:"= 0"})]}),e.jsxs("div",{className:"rounded-lg bg-white/70 p-2",children:[e.jsx("p",{className:"text-xs text-muted-foreground",children:"30°"}),e.jsx("p",{className:"text-violet-700",children:"â1/2"}),e.jsx("p",{className:"text-xs font-bold text-foreground mt-1",children:"= 1/2"})]}),e.jsxs("div",{className:"rounded-lg bg-white/70 p-2",children:[e.jsx("p",{className:"text-xs text-muted-foreground",children:"45°"}),e.jsx("p",{className:"text-violet-700",children:"â2/2"}),e.jsx("p",{className:"text-xs font-bold text-foreground mt-1",children:"â .707"})]}),e.jsxs("div",{className:"rounded-lg bg-white/70 p-2",children:[e.jsx("p",{className:"text-xs text-muted-foreground",children:"60°"}),e.jsx("p",{className:"text-violet-700",children:"â3/2"}),e.jsx("p",{className:"text-xs font-bold text-foreground mt-1",children:"â .866"})]}),e.jsxs("div",{className:"rounded-lg bg-white/70 p-2",children:[e.jsx("p",{className:"text-xs text-muted-foreground",children:"90°"}),e.jsx("p",{className:"text-violet-700",children:"â4/2"}),e.jsx("p",{className:"text-xs font-bold text-foreground mt-1",children:"= 1"})]})]}),e.jsx("p",{className:"text-sm font-bold text-violet-800 mb-3",children:"For Cosine (x-values) â count DOWN from 4:"}
6),e.jsxs("div",{className:"grid grid-cols-5 gap-2 text-center font-mono text-sm",children:[e.jsxs("div",{className:"rounded-lg bg-white/70 p-2",children:[e.jsx("p",{className:"text-xs text-muted-foreground",children:"0°"}),e.jsx("p",{className:"text-violet-700",children:"â4/2"}),e.jsx("p",{className:"text-xs font-bold text-foreground mt-1",children:"= 1"})]}),e.jsxs("div",{className:"rounded-lg bg-white/70 p-2",children:[e.jsx("p",{className:"text-xs text-muted-foreground",children:"30°"}),e.jsx("p",{className:"text-violet-700",children:"â3/2"}),e.jsx("p",{className:"text-xs font-bold text-foreground mt-1",children:"â .866"})]}),e.jsxs("div",{className:"rounded-lg bg-white/70 p-2",children:[e.jsx("p",{className:"text-xs text-muted-foreground",children:"45°"}),e.jsx("p",{className:"text-violet-700",children:"â2/2"}),e.jsx("p",{className:"text-xs font-bold text-foreground mt-1",children:"â .707"})]}),e.jsxs("div",{className:"rounded-lg bg-white/70 p-2",children:[e.jsx("p",{className:"text-xs text-muted-foreground",children:"60°"}),e.jsx("p",{className:"text-violet-700",children:"â1/2"}),e.jsx("p",{className:"text-xs font-bold text-foreground mt-1",children:"= 1/2"})]}),e.jsxs("div",{className:"rounded-lg bg-white/70 p-2",children:[e.jsx("p",{className:"text-xs text-muted-foreground",children:"90°"}),e.jsx("p",{className:"text-violet-700",children:"â0/2"}),e.jsx("p",{className:"text-xs font-bold text-foreground mt-1",children:"= 0"})]})]})]}),e.jsxs("div",{className:"rounded-xl border border-yellow-200 bg-gradient-to-br from-yellow-50 to-yellow-100/50 p-5",children:[e.jsxs("div",{className:"flex items-center gap-2 mb-2",children:[e.jsx(A,{className:"h-4 w-4 text-yellow-600 flex-shrink-0"}),e.jsx("span",{className:"text-sm font-bold text-yellow-800",children:"The Pattern"})]}),e.jsxs("p",{className:"text-sm text-yellow-900",children:["Sine goes ",e.jsx("strong",{children:"â0, â1, â2, â3, â4"})," all over 2. Cosine does the exact reverse. For other quadrants, keep the same values and adjust the sign using ASTC."]})]})]}),e.jsxs("section",{id:"finding-values",className:"mb-14 scroll-mt-20",children:[e.jsx("a",{href:"#finding-values",className:"group no-underline",children:e.jsxs("h2",{className:"text-2xl font-bold mb-4 flex items-center gap-2",children:[e.jsx("span",{className:"flex items-center justify-center w-8 h-8 rounded-full bg-primary text-white text-sm font-bold",children:"7"}),"Finding Values Using the Unit Circle",e.jsx(h,{className:"h-4 w-4 text-muted-foreground opacity-0 group-hover:opacity-100 transition-opacity"})]})}),e.jsx("p",{className:"text-muted-foreground mb-4",children:"Follow these steps to find the sine, cosine, or tangent of any angle:"}),e.jsxs("div",{className:"space-y-3 mb-6",children:[e.jsx("div",{className:"rounded-xl border border-border bg-card p-4",children:e.jsxs("div",{className:"flex items-center gap-3",children:[e.jsx("span",{className:"flex items-center justify-center w-8 h-8 rounded-full bg-violet-100 text-violet-700 text-sm font-bold",children:"1"}),e.jsxs("div",{children:[e.jsx("p",{className:"text-sm font-bold text-foreground",children:"Find the coterminal angle"}),e.jsx("p",{className:"text-xs text-muted-foreground mt-0.5",children:"If the angle is >360° or negative, add/subtract 360° to get an equivalent angle between 0° and 360°."})]})]})}),e.jsx("div",{className:"rounded-xl border border-border bg-card p-4",children:e.jsxs("div",{className:"flex items-center gap-3",children:[e.jsx("span",{className:"flex items-center justify-center w-8 h-8 rounded-full bg-violet-100 text-violet-700 text-sm font-bold",children:"2"}),e.jsxs("div",{children:[e.jsx("p",{className:"text-sm font-bold text-foreground",children:"Identify the quadrant"}),e.jsxs("p",{className:"text-xs text-muted-foreground mt-0.5",children:["This tells you the ",e.jsx("strong",{children:"signs"}),". Remember ",e.jsx("strong",{children:"ASTC"}),": All (Q1), Sine (Q2), Tangent (Q3), Cosine (Q4)."]})]})]})}),e.jsx("div",{className:"rounded-xl border border-border bg-card p-4",children:e.jsxs("div",{className:"flex items-center gap-3",children:[e.jsx("span",{className:"flex items-center justify-center w-8 h-8 rounded-full bg-violet-100 text-violet-700 text-sm font-bold",children:"3"}),e.jsxs("div",{children:[e.jsx("p",{className:"text-sm font-bold text-foreground",children:"Find the reference angle"}),e.jsxs("p",{className:"text-xs text-muted-foreground mt-0.5",children:[e.jsx("strong",{children:"Q1:"})," θ",e.jsx("sub",{children:"R"})," = θ ⢠",e.jsx("strong",{children:"Q2:"})," 180° â θ ⢠",e.jsx("strong",{children:"Q3:"})," θ â 180° ⢠",e.jsx("strong",{children:"Q4:"})," 360° â θ"]})]})]})}),e.jsx("div",{className:"rounded-xl border border-border bg-card p-4",children:e.jsxs("div",{className:"flex items-center gap-3",children:[e.jsx("span",{className:"flex items-center justify-center w-8 h-8 rounded-full bg-violet-100 text-violet-700 text-sm font-bold",children:"4"}),e.jsxs("div",{children:[e.jsx("p",{className:"text-sm font-bold text-foreground",children:"Use first-quadrant values + signs"}),e.jsx("p",{className:"text-xs text-muted-foreground mt-0.5",children:"Look up sin and cos for the reference angle from the special angles table, then apply the correct sign from step 2."})]})]})}),e.jsx("div",{className:"rounded-xl border border-border bg-card p-4",children:e.jsxs("div",{className:"flex items-center gap-3",children:[e.jsx("span",{className:"flex items-center justify-center w-8 h-8 rounded-full bg-violet-100 text-violet-700 text-sm font-bold",children:"5"}),e.jsxs("div",{children:[e.jsx("p",{className:"text-sm font-bold text-foreground",children:"Calculate tangent if needed"}),e.jsxs("p",{className:"text-xs text-muted-foreground mt-0.5",children:["tan θ = sin θ / cos θ. If cos θ = 0, tangent is ",e.jsx("strong",{children:"undefined"}),"."]})]})]})})]}),e.jsxs("div",{className:"rounded-xl border border-border bg-muted/20 p-5 font-mono text-sm space-y-1",children:[e.jsx("p",{className:"text-muted-foreground font-sans font-medium mb-2",children:"Example: Find sin(225°) and cos(225°)"}),e.jsx("p",{children:"  225° is in Quadrant III (180°â270°)"}),e.jsx("p",{children:"  Reference angle = 225° â 180° = 45°"}),e.jsx("p",{children:"  sin(45°) = â2/2, cos(45°) = â2/2"}),e.jsx("p",{children:"  In Q3: sin is negative, cos is negative"}),e.jsx("p",{className:"font-bold text-foreground",children:"  sin(225°) = ââ2/2, cos(225°) = ââ2/2"})]})]}),e.jsxs("section",{id:"worked-examples",className:"mb-14 scroll-mt-20",children:[e.jsx("a",{href:"#worked-examples",className:"group no-underline",children:e.jsxs("h2",{className:"text-2xl font-bold mb-4 flex items-center gap-2",children:[e.jsx("span",{className:"flex items-center justify-center w-8 h-8 rounded-full bg-primary text-white text-sm font-bold",children:"8"}),"Worked Examples",e.jsx(h,{className:"h-4 w-4 text-muted-foreground opacity-0 group-hover:opacity-100 transition-opacity"})]})}),e.jsxs("div",{className:"rounded-xl border border-border bg-card p-5 mb-5",children:[e.jsxs("div",{className:"flex items-center gap-2 mb-3",children:[e.jsx("span",{className:"text-sm font-bold text-foreground",children:"Example 1: Convert Degrees to Radians"}),e.jsx("span",{className:"rounded-full bg-green-100 text-green-700 px-2 py-0.5 text-[10px] font-semibold",children:"Basic"})]}),e.jsxs("p",{className:"text-sm text-muted-foreground mb-3",children:[e.jsx("strong",{children:"Problem:"})," Convert 45 degrees to radians."]}),e.jsxs("div",{className:"bg-muted/30 rounded-lg p-4 font-mono text-sm space-y-1",children:[e.jsx("p",{children:"Step 1: Recall the formula: radians = degrees à Ï/180"}),e.jsx("p",{children:"Step 2: Substitute: 45 à Ï/180"}),e.jsx("p",{children:"Step 3: Simplify: 45/180 = 1/4"}),e.jsx("p",{children:"Step 4: Multiply by Ï: 1/4 Ã Ï = Ï/4"}),e.jsx("p",{className:"font-bold text-foreground pt-2 border-t border-border mt-2",children:"Answer: Ï/4 radians"})]}),e.jsxs("p",{className:"text-xs text-muted-foreground mt-2",children:[e.jsx("strong",{children:"Method:"})," Degree to radian conversion"]})]}),e.jsxs("div",{className:"rounded-xl border border-border bg-card p-5 mb-5",children:[e.jsxs("div",{className:"flex items-center gap-2 mb-3",children:[e.jsx("span",{className:"text-sm font-bold text-foreground",children:"Example 2: Find Cos and Sin"}),e.jsx("span",{className:"rounded-full bg-green-100 text-green-700 px-2 py-0.5 text-[10px] font-semibold",children:"Basic"})]}),e.jsxs("p",{className:"text-sm text-muted-foreground mb-3",children:[e.jsx("strong",{children:"Problem:"})," Find cos(60°) and sin(60°)."]}),e.jsxs("div",{className:"bg-muted/30 rounded-lg p-4 font-mono text-sm space-y-1",children:[e.jsx("p",{children:"Step 1: Locate 60° on the unit circle â itâs a special angle in Q1"}),e.jsx("p",{children:"Step 2: From the special angles table, coordinates at 60° are (1/2, â3/2)"}),e.jsx("p",{children:"Step 3: x-coordinate = cos(60°) = 1/2"}),e.jsx("p",{children:"Step 4: y-coordinate = sin(60°) = â3/2"}),e.jsx("p",{className:"font-bold text-foreground pt-2 border-t border-border mt-2",children:"Answer: cos(60°) = 1/2, sin(60°) = â3/2"})]}),e.jsxs("p",{className:"text-xs text-muted-foreground mt-2",children:[e.jsx("strong",{children:"Method:"})," Unit circle coordinates"]})]}),e.jsxs("div",{className:"rounded-xl border border-border bg-card p-5 mb-5",children:[e.jsxs("div",{className:"flex items-center gap-2 mb-3",children:[e.jsx("span",{className:"text-sm font-bold text-foreground",children:"Example 3: Find Reference Angle"}),e.jsx("span",{className:"rounded-full bg-green-100 text-green-700 px-2 py-0.5 text-[10px] font-semibold",children:"Basic"})]}),e.jsxs("p",{className:"text-sm text-muted-foreground mb-3",children:[e.jsx("strong",{children:"Problem:"})," Find the reference angle for 150°."]}),e.jsxs("div",{className:"bg-muted/30 rounded-lg p-4 font-mono text-sm space-y-1",children:[e.jsx("p",{children:"Step 1: Identify the quadrant â 150° is between 90° and 180° â Q2"}),e.jsxs("p",{children:["Step 2: Formula for Q2: θ",e.jsx("sub",{children:"R"})," = 180° â θ"]}),e.jsxs("p",{children:["Step 3: θ",e.jsx("sub",{children:"R"})," = 180° â 150° = 30°"]}),e.jsx("p",{className:"font-bold text-foreground pt-2 border-t border-border mt-2",children:"Answer: 30°"})]}),e.jsxs("p",{className:"text-xs text-muted-foreground mt-2",children:[e.jsx("strong",{children:"Method:"})," Reference angle calculation"]})]}),e.jsxs("div",{className:"rounded-xl border border-border bg-card p-5 mb-5",children:[e.jsxs("div",{className:"flex items-center gap-2 mb-3",children:[e.jsx("span",{className:"text-sm font-bold text-foreground",children:"Example 4: Convert Radians to Degrees"}),e.jsx("span",{className:"rounded-full bg-green-100 text-green-700 px-2 py-0.5 text-[10px] font-semibold",children:"Basic"})]}),e.jsxs("p",{className:"text-sm text-muted-foreground mb-3",children:[e.jsx("strong",{children:"Problem:"})," Convert 3Ï/4 radians to degrees."]}),e.jsxs("div",{className:"bg-muted/30 rounded-lg p-4 font-mono text-sm space-y-1",children:[e.jsx("p",{children:"Step 1: Recall: degrees = radians à 180°/Ï"}),e.jsx("p",{children:"Step 2: Substitute: (3Ï/4) à 180°/Ï"}),e.jsx("p",{children:"Step 3: Cancel Ï: 3/4 à 180°"}),e.jsx("p",{children:"Step 4: Multiply: 3 à 45° = 135°"}),e.jsx("p",{className:"font-bold text-foreground pt-2 border-t border-border mt-2",children:"Answer: 135°"})]}),e.jsxs("p",{className:"text-xs text-muted-foreground mt-2",children:[e.jsx("strong",{children:"Method:"})," Radian to degree conversion"]})]}),e.jsxs("div",{className:"rounded-xl border border-border bg-card p-5 mb-5",children:[e.jsxs("div",{className:"flex items-center gap-2 mb-3",children:[e.jsx("span",{className:"text-sm font-bold text-foreground",children:"Example 5: Find Tangent"}),e.jsx("span",{className:"rounded-full bg-blue-100 text-blue-700 px-2 py-0.5 text-[10px] font-semibold",children:"Intermediate"})]}),e.jsxs("p",{className:"text-sm text-muted-foreground mb-3",children:[e.jsx("strong",{children:"Problem:"})," Find tan(Ï/3)."]}),e.jsxs("div",{className:"bg-muted/30 rounded-lg p-4 font-mono text-sm space-y-1",children:[e.jsx("p",{children:"Step 1: Recall tan = sin/cos"}),e.jsx("p",{children:"Step 2: Ï/3 radians = 60°"}),e.jsx("p",{children:"Step 3: sin(60°) = â3/2, cos(60°) = 1/2"}),e.jsx("p",{children:"Step 4: tan = (â3/2) / (1/2)"}),e.jsx("p",{children:"Step 5: Simplify: â3/2 à 2/1 = â3"}),e.jsx("p",{className:"font-bold text-foreground pt-2 border-t border-border mt-2",children:"Answer: â3"})]}),e.jsxs("p",{className:"text-xs text-muted-foreground mt-2",children:[e.jsx("strong",{children:"Method:"})," Tangent from unit circle"]})]}),e.jsxs("div",{className:"rounded-xl border border-border bg-card p-5 mb-5",children:[e.jsxs("div",{className:"flex items-center gap-2 mb-3",children:[e.jsx("span",{className:"text-sm font-bold text-foreground",children:"Example 6: Trig Values in Quadrant II"}),e.jsx("span",{className:"rounded-full bg-blue-100 text-blue-700 px-2 py-0.5 text-[10px] font-semibold",children:"Intermediate"})]}),e.jsxs("p",{className:"text-sm text-muted-foreground mb-3",children:[e.jsx("strong",{children:"Problem:"})," Find sin(150°) and cos(150°)."]}),e.jsxs("div",{className:"bg-muted/30 rounded-lg p-4 font-mono text-sm space-y-1",children:[e.jsx("p",{children:"Step 1: 150° is in Q2 (between 90° and 180°)"}),e.jsx("p",{children:"Step 2: Reference angle = 180° â 150° = 30°"}),e.jsx("p",{children:"Step 3: sin(30°) = 1/2, cos(30°) = â3/2"}),e.jsx("p",{children:"Step 4: In Q2, sine is positive, cosine is negative (ASTC)"}),e.jsx("p",{children:"Step 5: sin(150°) = +1/2, cos(150°) = ââ3/2"}),e.jsx("p",{className:"font-bold text-foreground pt-2 border-t border-border mt-2",children:"Answer: sin(150°) = 1/2, cos(150°) = ââ3/2"})]}),e.jsxs("p",{className:"text-xs text-muted-foreground mt-2",children:[e.jsx("strong",{children:"Method:"})," Reference angle + ASTC quadrant signs"]})]}),e.jsxs("div",{className:"rounded-xl border border-border bg-card p-5 mb-5",children:[e.jsxs("div",{className:"flex items-center gap-2 mb-3",children:[e.jsx("span",{className:"text-sm font-bold text-foreground",children:"Example 7: Trig Values in Quadrant III"}),e.jsx("span",{className:"rounded-full bg-amber-100 text-amber-700 px-2 py-0.5 text-[10px] font-semibold",children:"Advanced"})]}),e.jsxs("p",{className:"text-sm text-muted-foreground mb-3",children:[e.jsx("strong",{children:"Problem:"})," Find all trig values for 240°."]}),e.jsxs("div",{className:"bg-muted/30 rounded-lg p-4 font-mono text-sm space-y-1",children:[e.jsx("p",{children:"Step 1: 240° is in Q3 (between 180° and 270°)"}),e.jsx("p",{children:"Step 2: Reference angle = 240° â 180° = 60°"}),e.jsx("p",{children:"Step 3: sin(60°) = â3/2, cos(60°) = 1/2"}),e.jsx("p",{children:"Step 4: In Q3, both sin and cos are negative; tan is positive"}),e.jsx("p",{children:"Step 5: sin(240°) = ââ3/2, cos(240°) = â1/2"}),e.jsx("p",{children:"Step 6: tan(240°) = (ââ3/2) / (â1/2) = â3"}),e.jsx("p",{className:"font-bold text-foreground pt-2 border-t border-border mt-2",children:"Answer: sin = ââ3/2, cos = â1/2, tan = â3"})]}),e.jsxs("p",{className:"text-xs text-muted-foreground mt-2",children:[e.jsx("strong",{children:"Method:"})," Reference angle + ASTC for all three functions"]})]})]}),e.jsxs("section",{id:"memory-aids",className:"mb-14 scroll-mt-20",children:[e.jsx("a",{href:"#memory-aids",className:"group no-underline",children:e.jsxs("h2",{className:"text-2xl font-bold mb-4 flex items-center gap-2",children:[e.jsx("span",{className:"flex items-center justify-center w-8 h-8 rounded-full bg-primary text-white text-sm font-bold",children:"9"}),"Memory Aids",e.jsx(h,{className:"h-4 w-4 text-muted-foreground opacity-0 group-hover:opacity-100 transition-opacity"})]})}),e.jsxs("div",{className:"space-y-4",children:[e.jsxs("div",{className:"rounded-xl border border-yellow-200 bg-gradient-to-br from-yellow-50 to-yellow-100/50 p-5",children:[e.jsxs("div",{className:"flex items-center gap-2 mb-2",children:[e.jsx(A,{className:"h-4 w-4 text-yellow-600 flex-shrink-0"}),e.jsx("span",{className:"text-sm font-bold text-yellow
6-800",children:"âAll Students Take Calculusâ (ASTC)"})]}),e.jsxs("p",{className:"text-sm text-yellow-900",children:[e.jsx("strong",{children:"A"}),"ll trig functions positive in Q1, ",e.jsx("strong",{children:"S"}),"ine positive in Q2, ",e.jsx("strong",{children:"T"}),"angent positive in Q3, ",e.jsx("strong",{children:"C"}),"osine positive in Q4. This tells you the signs for any quadrant."]})]}),e.jsxs("div",{className:"rounded-xl border border-yellow-200 bg-gradient-to-br from-yellow-50 to-yellow-100/50 p-5",children:[e.jsxs("div",{className:"flex items-center gap-2 mb-2",children:[e.jsx(A,{className:"h-4 w-4 text-yellow-600 flex-shrink-0"}),e.jsx("span",{className:"text-sm font-bold text-yellow-800",children:"âx comes before y, Cosine before Sineâ"})]}),e.jsx("p",{className:"text-sm text-yellow-900",children:"Just as x comes before y in the alphabet, cosine (x-coordinate) comes before sine (y-coordinate) when writing the point (cos θ, sin θ)."})]}),e.jsxs("div",{className:"rounded-xl border border-yellow-200 bg-gradient-to-br from-yellow-50 to-yellow-100/50 p-5",children:[e.jsxs("div",{className:"flex items-center gap-2 mb-2",children:[e.jsx(A,{className:"h-4 w-4 text-yellow-600 flex-shrink-0"}),e.jsx("span",{className:"text-sm font-bold text-yellow-800",children:"ââ0, â1, â2, â3, â4 all over 2â"})]}),e.jsx("p",{className:"text-sm text-yellow-900",children:"Sine values for 0°, 30°, 45°, 60°, 90° follow this pattern. Cosine does the reverse (â4, â3, â2, â1, â0 all over 2)."})]}),e.jsxs("div",{className:"rounded-xl border border-yellow-200 bg-gradient-to-br from-yellow-50 to-yellow-100/50 p-5",children:[e.jsxs("div",{className:"flex items-center gap-2 mb-2",children:[e.jsx(A,{className:"h-4 w-4 text-yellow-600 flex-shrink-0"}),e.jsx("span",{className:"text-sm font-bold text-yellow-800",children:"â180 = Ïâ"})]}),e.jsx("p",{className:"text-sm text-yellow-900",children:"The core conversion: 180° = Ï radians. From this single fact you can derive all degree-radian conversions by multiplying or dividing by Ï/180."})]}),e.jsxs("div",{className:"rounded-xl border border-yellow-200 bg-gradient-to-br from-yellow-50 to-yellow-100/50 p-5",children:[e.jsxs("div",{className:"flex items-center gap-2 mb-2",children:[e.jsx(A,{className:"h-4 w-4 text-yellow-600 flex-shrink-0"}),e.jsx("span",{className:"text-sm font-bold text-yellow-800",children:"âReference = distance to nearest x-axisâ"})]}),e.jsxs("p",{className:"text-sm text-yellow-900",children:["The reference angle is always the acute angle to the ",e.jsx("strong",{children:"x-axis"})," (not the y-axis). Think of it as âhow far from the nearest horizontal?â"]})]})]})]}),e.jsxs("section",{id:"common-mistakes",className:"mb-14 scroll-mt-20",children:[e.jsx("a",{href:"#common-mistakes",className:"group no-underline",children:e.jsxs("h2",{className:"text-2xl font-bold mb-4 flex items-center gap-2",children:[e.jsx("span",{className:"flex items-center justify-center w-8 h-8 rounded-full bg-primary text-white text-sm font-bold",children:"10"}),"Common Mistakes to Avoid",e.jsx(h,{className:"h-4 w-4 text-muted-foreground opacity-0 group-hover:opacity-100 transition-opacity"})]})}),e.jsxs("div",{className:"space-y-4",children:[e.jsxs("div",{className:"rounded-xl border-2 border-red-200 bg-red-50/50 p-5",children:[e.jsx("p",{className:"text-sm font-bold text-red-800 mb-1",children:"Mixing Up Sine and Cosine"}),e.jsxs("p",{className:"text-sm text-red-700 mb-2",children:[e.jsx("strong",{children:"Wrong:"})," Thinking sine is the x-coordinate and cosine is the y-coordinate."]}),e.jsxs("p",{className:"text-sm text-green-700",children:[e.jsx("strong",{children:"Right:"})," Cosine = x-coordinate, Sine = y-coordinate. Remember: âx before y, cos before sin.â"]})]}),e.jsxs("div",{className:"rounded-xl border-2 border-red-200 bg-red-50/50 p-5",children:[e.jsx("p",{className:"text-sm font-bold text-red-800 mb-1",children:"Incorrect Quadrant Signs"}),e.jsxs("p",{className:"text-sm text-red-700 mb-2",children:[e.jsx("strong",{children:"Wrong:"})," sin(210°) = 1/2 (forgetting Q3 makes sine negative)"]}),e.jsxs("p",{className:"text-sm text-green-700",children:[e.jsx("strong",{children:"Right:"})," sin(210°) = â1/2. Always check which quadrant your angle is in and use ASTC to determine signs."]})]}),e.jsxs("div",{className:"rounded-xl border-2 border-red-200 bg-red-50/50 p-5",children:[e.jsx("p",{className:"text-sm font-bold text-red-800 mb
6-1",children:"Radian/Degree Conversion Errors"}),e.jsxs("p",{className:"text-sm text-red-700 mb-2",children:[e.jsx("strong",{children:"Wrong:"})," 60° à 180/Ï (multiplied by the wrong fraction)"]}),e.jsxs("p",{className:"text-sm text-green-700",children:[e.jsx("strong",{children:"Right:"})," To go from degrees to radians, multiply by ",e.jsx("strong",{children:"Ï/180"}),". To go from radians to degrees, multiply by ",e.jsx("strong",{children:"180/Ï"}),"."]})]}),e.jsxs("div",{className:"rounded-xl border-2 border-red-200 bg-red-50/50 p-5",children:[e.jsx("p",{className:"text-sm font-bold text-red-800 mb-1",children:"Incorrect Reference Angle"}),e.jsxs("p",{className:"text-sm text-red-700 mb-2",children:[e.jsx("strong",{children:"Wrong:"})," Reference angle for 300° = 300° â 180° = 120°"]}),e.jsxs("p",{className:"text-sm text-green-700",children:[e.jsx("strong",{children:"Right:"})," 300° is in Q4, so the reference angle = 360° â 300° = ",e.jsx("strong",{children:"60°"}),". Always use the correct formula for the quadrant."]})]}),e.jsxs("div",{className:"rounded-xl border-2 border-red-200 bg-red-50/50 p-5",children:[e.jsx("p",{className:"text-sm font-bold text-red-800 mb-1",children:"Forgetting Tangent is Sine/Cosine"}),e.jsxs("p",{className:"text-sm text-red-700 mb-2",children:[e.jsx("strong",{children:"Wrong:"})," Trying to memorize tangent values independently for every angle."]}),e.jsxs("p",{className:"text-sm text-green-700",children:[e.jsx("strong",{children:"Right:"})," Just remember tan θ = sin θ / cos θ. Once you know sine and cosine, tangent follows automatically."]})]}),e.jsxs("div",{className:"rounded-xl border-2 border-red-200 bg-red-50/50 p-5",children:[e.jsx("p",{className:"text-sm font-bold text-red-800 mb-1",children:"Forgetting Tangent is Undefined at 90° and 270°"}),e.jsxs("p",{className:"text-sm text-red-700 mb-2",children:[e.jsx("strong",{children:"Wrong:"})," tan(90°) = 1 or tan(90°) = 0"]}),e.jsxs("p",{className:"text-sm text-green-700",children:[e.jsx("strong",{children:"Right:"})," tan(90°) is ",e.jsx("strong",{children:"undefined"})," because cos(90°) = 0 and you cannot divide by zero. The same applies to 270°."]})]}),e.jsxs("div",{className:"rounded-xl border-2 border-red-200 bg-red-50/50 p-5",children:[e.jsx("p",{className:"text-sm font-bold text-red-800 mb-1",children:"Not Simplifying Coordinates"}),e.jsxs("p",{className:"text-sm text-red-700 mb-2",children:[e.jsx("strong",{children:"Wrong:"})," Leaving cos(0°) = â4/2 without simplifying"]}),e.jsxs("p",{className:"text-sm text-green-700",children:[e.jsx("strong",{children:"Right:"})," â4/2 = 2/2 = ",e.jsx("strong",{children:"1"}),". Always simplify radicals and fractions in your final answer."]})]}),e.jsxs("div",{className:"rounded-xl border-2 border-red-200 bg-red-50/50 p-5",children:[e.jsx("p",{className:"text-sm font-bold text-red-800 mb-1",children:"Measuring Reference Angle to the Y-Axis"}),e.jsxs("p",{className:"text-sm text-red-700 mb-2",children:[e.jsx("strong",{children:"Wrong:"})," Reference angle for 120° = 120° â 90° = 30° (measured from y-axis)"]}),e.jsxs("p",{className:"text-sm text-green-700",children:[e.jsx("strong",{children:"Right:"})," Reference angles are ",e.jsx("strong",{children:"always measured from the x-axis"}),". For 120° (Q2): 180° â 120° = ",e.jsx("strong",{children:"60°"}),"."]})]})]})]}),e.jsxs("section",{id:"revision-summary",className:"mb-14 scroll-mt-20",children:[e.jsx("a",{href:"#revision-summary",className:"group no-underline",children:e.jsxs("h2",{className:"text-2xl font-bold mb-4 flex items-center gap-2",children:[e.jsx("span",{className:"flex items-center justify-center w-8 h-8 rounded-full bg-primary text-white text-sm font-bold",children:"11"}),"Quick Revision Summary",e.jsx(h,{className:"h-4 w-4 text-muted-foreground opacity-0 group-hover:opacity-100 transition-opacity"})]})}),e.jsx("div",{className:"rounded-xl border border-border bg-muted/30 p-6",children:e.jsxs("ul",{className:"space-y-2 text-sm text-muted-foreground",children:[e.jsxs("li",{className:"flex items-start gap-2",children:[e.jsx(p,{className:"h-4 w-4 text-green-500 flex-shrink-0 mt-0.5"})," The unit circle has ",e.jsx("strong",{children:"radius 1"}),", centered at the origin. Equation: x² + y² = 1."]}),e.jsxs("li",{className:"flex items-start gap-2",children:[e.jsx(p,{className:"h-4 w-4 text-green-500 flex-shrink-0 mt-0.5"})," Any point on it is ",e.jsx("strong",{children:"(cos θ, sin θ)"}),". x = cosine, y = sine."]}),e.jsxs("li",{className:"flex items-start gap-2",children:[e.jsx(p,{className:"h-4 w-4 text-green-500 flex-shrink-0 mt-0.5"})," ",e.jsx("strong",{children:"tan θ = sin θ / cos θ"}),". Undefined when cos θ = 0."]}),e.jsxs("li",{className:"flex items-start gap-2",children:[e.jsx(p,{className:"h-4 w-4 text-green-500 flex-shrink-0 mt-0.5"})," ",e.jsx("strong",{children:"180° = Ï radians"}),". Multiply by Ï/180 or 180/Ï to convert."]}),e.jsxs("li",{className:"flex items-start gap-2",children:[e.jsx(p,{className:"h-4 w-4 text-green-500 flex-shrink-0 mt-0.5"})," Memorize the five special angles: ",e.jsx("strong",{children:"0°, 30°, 45°, 60°, 90°"})," and their coordinates."]}),e.jsxs("li",{className:"flex items-start gap-2",children:[e.jsx(p,{className:"h-4 w-4 text-green-500 flex-shrink-0 mt-0.5"})," Use the âAll Over 2â trick: sin goes â0 to â4 over 2; cos reverses."]}),e.jsxs("li",{className:"flex items-start gap-2",children:[e.jsx(p,{className:"h-4 w-4 text-green-500 flex-shrink-0 mt-0.5"})," ",e.jsx("strong",{children:"ASTC"})," (All Students Take Calculus) gives you the signs in each quadrant."]}),e.jsxs("li",{className:"flex items-start gap-2",children:[e.jsx(p,{className:"h-4 w-4 text-green-500 flex-shrink-0 mt-0.5"})," The ",e.jsx("strong",{children:"reference angle"})," is always acute and measured from the ",e.jsx("strong",{children:"x-axis"}),"."]}),e.jsxs("li",{className:"flex items-start gap-2",children:[e.jsx(p,{className:"h-4 w-4 text-green-500 flex-shrink-0 mt-0.5"})," For other quadrants: use first-quadrant values + adjust signs with ASTC."]}),e.jsxs("li",{className:"flex items-start gap-2",children:[e.jsx(p,{className:"h-4 w-4 text-green-500 flex-shrink-0 mt-0.5"})," Always simplify radicals and fractions in your final answers."]})]})})]}),e.jsxs("section",{id:"faq",className:"mb-14 scroll-mt-20",children:[e.jsx("h2",{className:"text-2xl font-bold mb-6",children:"Frequently Asked Questions"}),e.jsx("div",{className:"space-y-4",children:$.map((l,T)=>e.jsxs("div",{className:"rounded-xl border border-border p-5",children:[e.jsx("p",{className:"font-semibold text-foreground mb-2",children:l.question}),e.jsx("p",{className:"text-sm text-muted-foreground",children:l.answer})]},T))})]}),e.jsxs("section",{id:"quiz",className:"mb-14 scroll-mt-20",children:[e.jsx("h2",{className:"text-2xl font-bold mb-6",children:"Practice Quiz"}),e.jsx(ae,{headless:!0})]}),e.jsxs("section",{className:"mb-14",children:[e.jsx("h2",{className:"text-2xl font-bold mb-4",children:"Study Tips"}),e.jsxs("ol",{className:"space-y-3 text-sm text-muted-foreground list-decimal list-inside",children:[e.jsxs("li",{children:[e.jsx("strong",{children:"Memorize the first-quadrant values first"})," â everything else is derived from these five special angles using reference angles and ASTC."]}),e.jsxs("li",{children:[e.jsx("strong",{children:"Use the interactive explorer above"})," â move the slider around the full circle to build intuition for how sin and cos change."]}),e.jsxs("li",{children:[e.jsx("strong",{children:"Practice converting between radians and degrees"})," â start with the common angles and work up to less familiar ones."]}),e.jsxs("li",{children:[e.jsx("strong",{children:"Draw the unit circle by hand"})," â this is one of the best ways to internalize the coordinates and quadrant signs."]}),e.jsxs("li",{children:[e.jsx("strong",{children:"Check your signs last"})," â first find the magnitude using the reference angle, then apply the correct sign using ASTC."]})]})]}),e.jsxs("section",{className:"mb-4",children:[e.jsx("h2",{className:"text-2xl font-bold mb-4",children:"Related Topics"}),e.jsxs("div",{className:"grid sm:grid-cols-2 gap-3",children:[e.jsxs(C,{to:"/resources/mathematics/right-triangle-trig",className:"rounded-xl border border-border p-4 hover:border-primary/40 transition-colors group",children:[e.jsx("p",{className:"font-semibold text-foreground group-hover:text-primary transition-colors",children:"Right Triangle Trigonometry"}),e.jsx("p",{className:"text-xs text-muted-foreground mt-1",children:"SOH-CAH-TOA, finding sides and angles, inverse trig functions"})]}),e.jsxs(C,{to:"/resources/mathematics/angles-and-triangles",className:"rounded-xl border border-border p-4 hover:border-primary/40 transition-colors group",children:[e.jsx("p",{className:"font-semibold text-foreground group-hover:text-primary transition-colors",children:"Angles and Triangles"}),e.jsx("p",{className:"text-xs text-muted-foreground mt-1",children:"Triangle properties, angle relationships, and congruence"})]}),e.jsxs(C,{to:"/resources/mathematics/functions-and-graphs",className:"rounded-xl border border-border p-4 hover:border-primary/40 transition-colors group",children:[e.jsx("p",{className:"font-semibold text-foreground group-hover:text-primary transition-colors",children:"Functions and Graphs"}),e.jsx("p",{className:"text-xs text-muted-foreground mt-1",children:"Function notation, types, transformations, and graphing"})]}),e.jsxs(C,{to:"/resources/mathematics/quadratic-equations",className:"rounded-xl border border-border p-4 hover:border-primary/40 transition-colors group",children:[e.jsx("p",{className:"font-semibold text-foreground group-hover:text-primary transition-colors",children:"Quadratic Equations"}),e.jsx("p",{className:"text-xs text-muted-foreground mt-1",children:"Solving, graphing, and applying quadratic equations"})]})]})]})]})]})})]})}export{ke as default};
Line numbers count LF bytes from the start of the resource, as the search results do. Vendor segments are library code the classifier recognised; they are stored but not indexed. Bytes are shown as Latin1 characters, one per byte.