Pre – Calculus
Unit 4
Section 5.5: Multiple Angle Identities
Objectives:
Use double angle and half angle identities to evaluate trigonometric expressions and solve trigonometric equations.
Double Angle Identities
𝜋
Example 1: Find sin2θ, cos2θ, and tan2θ on the interval�0, �.
a) if sin 𝜃 =
3
2
4
Example 2: Solve double angle equations on the interval (0,2𝜋)
a) cos2θ - cosθ = 2
b) cos 𝜃 =
5
13
b) tan2θ + tanθ = 0
Half Angle Identities
𝜃
** The sign of each identity that involves the ± symbol is determined by checking the quadrant in which the terminal side of lies.
2
Example 5: Find the exact value of
a) sin 22.5°
b) tan
𝜋
c) cos 67.5°
12
Example 6: Solve half angle equations on the interval [0, 2π)
𝜃
a) 2 sin = sin θ
2
𝑥
b) sin2 = cos2
2
𝑥
2