Trigonometry — Formula Sheet

In a 45°-45°-90° triangle, both shorter sides are equal and the hypotenuse is √2 times the shorter side

In a 30°-60°-90° triangle, sides are in the ratio 1

√3 : 2

Sine (sin) = Opposite side / Hypotenuse

Cosine (cos) = Adjacent side / Hypotenuse

Tangent (tan) = Opposite side / Adjacent side

sin 0° = 0, sin 30° = 1/2, sin 45° = 1/√2, sin 60° = √3/2, sin 90° = 1

cos 0° = 1, cos 30° = √3/2, cos 45° = 1/√2, cos 60° = 1/2, cos 90° = 0

tan 0° = 0, tan 30° = 1/√3, tan 45° = 1, tan 60° = √3, tan 90° = undefined

In 45°-45°-90° triangles, sides are in ratio 1:1:√2.

In 30°-60°-90° triangles, sides are in ratio 1:√3:2 (shortest to longest).

sin θ = opposite side/hypotenuse in a right triangle.

cos θ = adjacent side/hypotenuse in a right triangle.

tan θ = opposite side/adjacent side = sin θ/cos θ.