Introduction to Trigonometry — sin, cos and tan

The three ratios (right-angled triangle)

For an angle θ, relative to the sides Opposite, Adjacent and Hypotenuse:

• sin θ = Opposite / Hypotenuse
• cos θ = Adjacent / Hypotenuse
• tan θ = Opposite / Adjacent

Remember it as SOH-CAH-TOA.

Standard angles

sin 0°=0, sin 30°=½, sin 45°=1/√2, sin 60°=√3/2, sin 90°=1. For cos, read the same values backwards (cos 0°=1 ... cos 90°=0). tan θ = sin θ / cos θ.

Worked example

A ladder leans against a wall at 60°. Its foot is 2 m from the wall. How long is the ladder?

cos 60° = adjacent / hypotenuse → ½ = 2 / L → L = 4 m.

Exam tip: Draw the triangle and label Opposite, Adjacent, Hypotenuse before choosing a ratio.