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trigonometry.html
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<!DOCTYPE html>
<html lang="en">
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<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>FlashMath | trigonometry</title>
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<main class="main-content">
<header class="header">
<h1>FlashMath | trigonometry</h1>
</header>
<div style="margin-top: 80px;"></div>
<h2 id = "one">fundamental trigonometric identities</h2>
<section class="flashcard" style="grid-template-columns: repeat(6, 1fr); width: 98%;">
<div class="card" style="aspect-ratio: 3/1;">
<div class="card__inner">
<div class="card__face card__front">
sin²θ + cos²θ =
</div>
<div class="card__face card__back">
1
</div>
</div>
</div>
<div class="card" style="aspect-ratio: 3/1;">
<div class="card__inner">
<div class="card__face card__front">
1 + tan²θ =
</div>
<div class="card__face card__back">
sec²θ
</div>
</div>
</div>
<div class="card" style="aspect-ratio: 3/1;">
<div class="card__inner">
<div class="card__face card__front">
1 + cot²θ =
</div>
<div class="card__face card__back">
csc²θ
</div>
</div>
</div>
<div class="card" style="aspect-ratio: 3/1;">
<div class="card__inner">
<div class="card__face card__front">
sin(-θ) =
</div>
<div class="card__face card__back">
-sinθ
</div>
</div>
</div>
<div class="card" style="aspect-ratio: 3/1;">
<div class="card__inner">
<div class="card__face card__front">
cos(-θ) =
</div>
<div class="card__face card__back">
cosθ
</div>
</div>
</div>
<div class="card" style="aspect-ratio: 3/1;">
<div class="card__inner">
<div class="card__face card__front">
tan(-θ) =
</div>
<div class="card__face card__back">
-tanθ
</div>
</div>
</div>
</section>
<br>
<h2 id = "two">reciprocal identities</h2>
<section class="flashcard" style="grid-template-columns: repeat(6, 1fr); width: 98%;">
<div class="card" style="aspect-ratio: 3/1;">
<div class="card__inner">
<div class="card__face card__front">
sinθ =
</div>
<div class="card__face card__back">
1/cscθ
</div>
</div>
</div>
<div class="card" style="aspect-ratio: 3/1;">
<div class="card__inner">
<div class="card__face card__front">
cosθ =
</div>
<div class="card__face card__back">
1/secθ
</div>
</div>
</div>
<div class="card" style="aspect-ratio: 3/1;">
<div class="card__inner">
<div class="card__face card__front">
tanθ =
</div>
<div class="card__face card__back">
sinθ/cosθ
</div>
</div>
</div>
<div class="card" style="aspect-ratio: 3/1;">
<div class="card__inner">
<div class="card__face card__front">
cotθ =
</div>
<div class="card__face card__back">
cosθ/sinθ
</div>
</div>
</div>
<div class="card" style="aspect-ratio: 3/1;">
<div class="card__inner">
<div class="card__face card__front">
secθ =
</div>
<div class="card__face card__back">
1/cosθ
</div>
</div>
</div>
<div class="card" style="aspect-ratio: 3/1;">
<div class="card__inner">
<div class="card__face card__front">
cscθ =
</div>
<div class="card__face card__back">
1/sinθ
</div>
</div>
</div>
</section>
<br>
<h2 id = "three">angle sum and difference identities</h2>
<section class="flashcard" style="grid-template-columns: repeat(6, 1fr); width: 98%;">
<div class="card merge" style="aspect-ratio: 6/1;">
<div class="card__inner">
<div class="card__face card__front">
sin(A ± B) =
</div>
<div class="card__face card__back">
sinAcosB ± cosAsinB
</div>
</div>
</div>
<div class="card merge" style="aspect-ratio: 6/1;">
<div class="card__inner">
<div class="card__face card__front">
cos(A ± B) =
</div>
<div class="card__face card__back">
cosAcosB ∓ sinAsinB
</div>
</div>
</div>
<div class="card merge" style="aspect-ratio: 6/1;">
<div class="card__inner">
<div class="card__face card__front">
tan(A ± B) =
</div>
<div class="card__face card__back">
(tanA ± tanB) / (1 ∓ tanAtanB)
</div>
</div>
</div>
<div class="card merge" style="aspect-ratio: 6/1;">
<div class="card__inner">
<div class="card__face card__front">
sin(2θ) =
</div>
<div class="card__face card__back">
2sinθcosθ
</div>
</div>
</div>
<div class="card merge" style="aspect-ratio: 6/1;">
<div class="card__inner">
<div class="card__face card__front">
cos(2θ) =
</div>
<div class="card__face card__back">
cos²θ - sin²θ
</div>
</div>
</div>
<div class="card merge" style="aspect-ratio: 6/1;">
<div class="card__inner">
<div class="card__face card__front">
tan(2θ) =
</div>
<div class="card__face card__back">
2tanθ / (1 - tan²θ)
</div>
</div>
</div>
</section>
<br>
<h2 id = "four">product-to-sum identities</h2>
<section class="flashcard" style="grid-template-columns: repeat(6, 1fr); width: 98%;">
<div class="card merge" style="aspect-ratio: 6/1;">
<div class="card__inner">
<div class="card__face card__front">
sinAcosB =
</div>
<div class="card__face card__back">
1/2[sin(A + B) + sin(A - B)]
</div>
</div>
</div>
<div class="card merge" style="aspect-ratio: 6/1;">
<div class="card__inner">
<div class="card__face card__front">
cosAcosB =
</div>
<div class="card__face card__back">
1/2[cos(A + B) + cos(A - B)]
</div>
</div>
</div>
<div class="card merge" style="aspect-ratio: 6/1;">
<div class="card__inner">
<div class="card__face card__front">
sinAsinB =
</div>
<div class="card__face card__back">
1/2[cos(A - B) - cos(A + B)]
</div>
</div>
</div>
</section>
<br>
<h2 id = "five">sum-to-product identities</h2>
<section class="flashcard" style="grid-template-columns: repeat(6, 1fr); width: 98%;">
<div class="card merge" style="aspect-ratio: 6/1;">
<div class="card__inner">
<div class="card__face card__front">
sinA + sinB =
</div>
<div class="card__face card__back">
2sin[(A + B)/2]cos[(A - B)/2]
</div>
</div>
</div>
<div class="card merge" style="aspect-ratio: 6/1;">
<div class="card__inner">
<div class="card__face card__front">
cosA + cosB =
</div>
<div class="card__face card__back">
2cos[(A + B)/2]cos[(A - B)/2]
</div>
</div>
</div>
<div class="card merge" style="aspect-ratio: 6/1;">
<div class="card__inner">
<div class="card__face card__front">
sinA - sinB =
</div>
<div class="card__face card__back">
2cos[(A + B)/2]sin[(A - B)/2]
</div>
</div>
</div>
</section>
<br>
<h2 id = "six">half-angle identities</h2>
<section class="flashcard" style="grid-template-columns: repeat(6, 1fr); width: 98%;">
<div class="card merge" style="aspect-ratio: 6/1;">
<div class="card__inner">
<div class="card__face card__front">
sin²(θ/2) =
</div>
<div class="card__face card__back">
(1 - cosθ) / 2
</div>
</div>
</div>
<div class="card merge" style="aspect-ratio: 6/1;">
<div class="card__inner">
<div class="card__face card__front">
cos²(θ/2) =
</div>
<div class="card__face card__back">
(1 + cosθ) / 2
</div>
</div>
</div>
<div class="card merge" style="aspect-ratio: 6/1;">
<div class="card__inner">
<div class="card__face card__front">
tan²(θ/2) =
</div>
<div class="card__face card__back">
(1 - cosθ) / (1 + cosθ)
</div>
</div>
</div>
<div class="card merge" style="aspect-ratio: 6/1;">
<div class="card__inner">
<div class="card__face card__front">
sin(θ/2) =
</div>
<div class="card__face card__back">
±√[(1 - cosθ) / 2]
</div>
</div>
</div>
<div class="card merge" style="aspect-ratio: 6/1;">
<div class="card__inner">
<div class="card__face card__front">
cos(θ/2) =
</div>
<div class="card__face card__back">
±√[(1 + cosθ) / 2]
</div>
</div>
</div>
<div class="card merge" style="aspect-ratio: 6/1;">
<div class="card__inner">
<div class="card__face card__front">
tan(θ/2) =
</div>
<div class="card__face card__back">
sinθ / (1 + cosθ)
</div>
</div>
</div>
</section>
<br>
<h2 id = "seven">triple angle identities</h2>
<section class="flashcard" style="grid-template-columns: repeat(6, 1fr); width: 98%;">
<div class="card merge" style="aspect-ratio: 6/1;">
<div class="card__inner">
<div class="card__face card__front">
sin(3θ) =
</div>
<div class="card__face card__back">
3sinθ - 4sin³θ
</div>
</div>
</div>
<div class="card merge" style="aspect-ratio: 6/1;">
<div class="card__inner">
<div class="card__face card__front">
cos(3θ) =
</div>
<div class="card__face card__back">
4cos³θ - 3cosθ
</div>
</div>
</div>
<div class="card merge" style="aspect-ratio: 6/1;">
<div class="card__inner">
<div class="card__face card__front">
tan(3θ) =
</div>
<div class="card__face card__back">
(3tanθ - tan³θ) / (1 - 3tan²θ)
</div>
</div>
</div>
<div class="card merge" style="aspect-ratio: 6/1;">
<div class="card__inner">
<div class="card__face card__front">
sin(3A) =
</div>
<div class="card__face card__back">
3sinA - 4sin³A
</div>
</div>
</div>
<div class="card merge" style="aspect-ratio: 6/1;">
<div class="card__inner">
<div class="card__face card__front">
cos(3A) =
</div>
<div class="card__face card__back">
4cos³A - 3cosA
</div>
</div>
</div>
<div class="card merge" style="aspect-ratio: 6/1;">
<div class="card__inner">
<div class="card__face card__front">
tan(3A) =
</div>
<div class="card__face card__back">
(3tanA - tan³A) / (1 - 3tan²A)
</div>
</div>
</div>
</section>
<br>
<h2 id = "eight">even-odd identities</h2>
<section class="flashcard" style="grid-template-columns: repeat(6, 1fr); width: 98%;">
<div class="card" style="aspect-ratio: 3/1;">
<div class="card__inner">
<div class="card__face card__front">
sin(-θ) =
</div>
<div class="card__face card__back">
-sinθ
</div>
</div>
</div>
<div class="card" style="aspect-ratio: 3/1;">
<div class="card__inner">
<div class="card__face card__front">
cos(-θ) =
</div>
<div class="card__face card__back">
cosθ
</div>
</div>
</div>
<div class="card" style="aspect-ratio: 3/1;">
<div class="card__inner">
<div class="card__face card__front">
tan(-θ) =
</div>
<div class="card__face card__back">
-tanθ
</div>
</div>
</div>
<div class="card" style="aspect-ratio: 3/1;">
<div class="card__inner">
<div class="card__face card__front">
cot(-θ) =
</div>
<div class="card__face card__back">
-cotθ
</div>
</div>
</div>
<div class="card" style="aspect-ratio: 3/1;">
<div class="card__inner">
<div class="card__face card__front">
sec(-θ) =
</div>
<div class="card__face card__back">
secθ
</div>
</div>
</div>
<div class="card" style="aspect-ratio: 3/1;">
<div class="card__inner">
<div class="card__face card__front">
csc(-θ) =
</div>
<div class="card__face card__back">
-cscθ
</div>
</div>
</div>
</section>
<br>
<h2 id = "nine">miscellaneous identities</h2>
<section class="flashcard" style="grid-template-columns: repeat(6, 1fr); width: 98%;">
<div class="card" style="aspect-ratio: 3/1;">
<div class="card__inner">
<div class="card__face card__front">
sin(π/2 - θ) =
</div>
<div class="card__face card__back">
cosθ
</div>
</div>
</div>
<div class="card" style="aspect-ratio: 3/1;">
<div class="card__inner">
<div class="card__face card__front">
cos(π/2 - θ) =
</div>
<div class="card__face card__back">
sinθ
</div>
</div>
</div>
<div class="card" style="aspect-ratio: 3/1;">
<div class="card__inner">
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tan(π/2 - θ) =
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cotθ
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cot(π/2 - θ) =
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tanθ
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sec(π/2 - θ) =
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cscθ
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csc(π/2 - θ) =
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secθ
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