This document discusses double angle identities for sine, cosine, and tangent. It provides the formulas for sin(2θ), cos(2θ), and tan(2θ) in terms of sin(θ) and cos(θ). The document also includes examples of using the double angle identities to evaluate trigonometric functions and solve equations.
1. Exercise #18
Double Angle Identities
sin 2 2sin cos
cos 2 cos 2 sin 2
OR 2cos 1
2
1 2sin 2
OR
2 tan
tan 2
1 tan 2
Example
Evaluate cos120 using the double angle formula.
Example
4 3
If sin and cos , find tan 2 .
5 5
2. Example
Solve sin 2 sin over the interval 0, 2 .
Example
Given that cos 0.99 , evaluate cos .
20 10
Try
Evaluate cos given that cos 0.97 .
7 14