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 