Use the exact values of the trigonometric ratios of 30°, 45° and 60°

Follow this one with me, a step at a time. Try to guess each step first.

Worked example 1

Find the exact value of 4 cos² 60° − 3 sin² 45°.

Remember: Write down the exact value of each ratio, square it, then multiply by the number in front.

From the exact values, cos² 60° = 14 and sin² 45° = 1/2.
Substituting gives 4 × 14 − 3 × 1/2.
The exact value is −1/2.

Common mistakes

Squared the number in front as well. In 2 sin² θ only the ratio is squared.
Used the ratio itself. sin² θ means (sin θ)², so the value must be squared.
Added where the expression subtracts.