5.4 Sum and Difference Formulas

In this section students will use sum and difference formulas to evaluate trigonometric functions, verify identities, and solve trigonometric equations.

Section 5.4, Sum and Difference Formulas, pg. 368

Example 1

Find the exact value of cos75

Section 5.4, Sum and Difference Formulas, pg. 368

Example 2

Find the exact value of sin12

Section 5.4, Sum and Difference Formulas, pg. 368

Example 3

Find the exact value of sin(u+v) given

, where and

where

sinu 4

50

2 u

cosv

12

13 2

v

Section 5.4, Sum and Difference Formulas, pg. 368

Example 5

Prove the cofunction identity cos( ) sin2

x x

Section 5.4, Sum and Difference Formulas, pg. 368

Example 6

Simplify the expression.

a. b.cos( )

3

2tan( ) 3

Section 5.4, Sum and Difference Formulas, pg. 368

Example 7

Find all solutions of in the interval

sin( ) sin( )x x 4 4

1

[ , )0 2