Sin, Cos, Tan in Right-Angled Triangles

Labelling the triangle

For angle θ:
Opposite = side opposite θ
Adjacent = side next to θ, not hypotenuse
Hypotenuse = longest side

Ratios

sin θ = Opposite / Hypotenuse

cos θ = Adjacent / Hypotenuse

tan θ = Opposite / Adjacent

Memory aid: SOH CAH TOA

Exact values

sin 30° = 1/2, cos 30° = √3/2, tan 30° = 1/√3

sin 45° = 1/√2, cos 45° = 1/√2, tan 45° = 1

sin 60° = √3/2, cos 60° = 1/2, tan 60° = √3

Discussion

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