1

Pre-CalculusChapter 5

Analytic Trigonometry

2

5.4 Sum & Difference Formulas

Objectives: Use sum and difference formulas to

evaluate trigonometric functions, verify identities, and solve trigonometric equations.

3

Consider This…. Determine whether each equation is

true or false. Justify your answer.

1cos30cos29cos.2

60sin14sin74sin.1

4

Sum & Difference Formulas Sine

Cosine

Signs are the same.

Signs change.

5

Sum & Difference Formulas Tangent

6

Example 1 Find the exact value of cos 75°.

Check your answer with a calculator.

7

Example 2 Find the exact value of .

12sin

8

Example 3 Simplify.

47tan152tan1

47tan152tan.2

80sin110cos80cos110sin.1

9

Example 4 Find the exact value of sin (u + v)

given

where and

where

5

4sin u

20

u

13

12cos v

v2

10

Example 5 Prove the cofunction identity.

xx sin

2cos

11

Example 6 Simplify each expression.

3tan.2

2

3cos.1

12

Example 7 Find all solutions of the equation in

the interval [0, 2π).

14

sin4

sin

xx

13

Homework 5.4 Worksheet 5.4