Mathematics · Trigonometry

Sin, Cos, Tan
& Pythagoras

Master the fundamentals of trigonometry with 20 carefully designed questions. Study the cheat sheet below, then test yourself.

// Core Ratios — Cheat Sheet
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Super Memory Key

The #1 mnemonic used worldwide to remember all three ratios at once:

SOH · CAH · TOA
SOH = Sin = Opposite/Hypotenuse  |  CAH = Cos = Adjacent/Hypotenuse  |  TOA = Tan = Opposite/Adjacent
θ Hypotenuse (H) Opposite (O) Adjacent (A)

Right Triangle Ratios

sin θ = O ÷ H  (Opposite / Hypotenuse)
cos θ = A ÷ H  (Adjacent / Hypotenuse)
tan θ = O ÷ A  (Opposite / Adjacent)
Pythagoras a² + b² = c²  (c = hypotenuse)
SINE
sin θ = O/H
Sin = Opposite over Hypotenuse
Memory: "SOH"
COSINE
cos θ = A/H
Cos = Adjacent over Hypotenuse
Memory: "CAH"
TANGENT
tan θ = O/A
Tan = Opposite over Adjacent
Memory: "TOA"
PYTHAGORAS
a² + b² = c²
c = hypotenuse (longest side)
Memory: "Leg²+Leg²=Hyp²"
// Special Angles — Must Memorize!
Angle (°) sin θ cos θ tan θ
0°010
30°1/2√3/21/√3
45°1/√21/√21
60°√3/21/2√3
90°10undefined
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Pro Trick — sin & cos at 30° and 60°

sin 30° = cos 60° = 1/2    |    sin 60° = cos 30° = √3/2
They swap! sin and cos are "complementary" — sin θ = cos(90°−θ) COMPLEMENTARY PAIR

20 Practice Questions
0 / 20 answered

Quiz Complete 🎉

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