Mr. Integral
Math notes/Pre-Calculus/Trigonometry

Ratios in a Right Triangle — Essentials

ESSENTIALS   ·   FREE

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The three ratios

FunctionRatio
sin⁡θ\sin\thetaopposite / hypotenuse
cos⁡θ\cos\thetaadjacent / hypotenuse
tan⁡θ\tan\thetaopposite / adjacent

The other three are these upside down: cot⁡θ=1/tan⁡θ\cot\theta = 1/\tan\theta, sec⁡θ=1/cos⁡θ\sec\theta = 1/\cos\theta, csc⁡θ=1/sin⁡θ\csc\theta = 1/\sin\theta.

Traps

TrapRule
"Opposite" moves with the anglename the sides from the angle you are using, not from the picture
Impossible valuessin⁡θ\sin\theta and cos⁡θ\cos\theta never exceed 11

sin⁡θ=cos⁡(90∘−θ)\sin\theta = \cos(90^\circ - \theta) - the other acute angle sees the same legs swapped.