Identities: Pythagorean and Sum and Difference Section 7.1 Identities: Pythagorean and Sum and Difference Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.

Objectives State the Pythagorean identities. Simplify and manipulate expressions containing trigonometric expressions. Use the sum and difference identities to find function values.

Basic Identities

Pythagorean Identities Recall the equation of a unit circle in the xy-plane

Pythagorean Identities We can develop two other Pythagorean identities.

Pythagorean Identities Equivalent Forms Pythagorean Identities

Example Factor and simplify Solution:

Example Simplify each of the following trigonometric expressions. Solution:

Example (cont)

Example Add and simplify Solution:

Example Express as a trigonometric function of  without using radicals by letting x = 3 tan Assume that 0 <  < π/2. Then find sin  and cos . Solution:

Example (cont)

Sum and Difference Identities

Example Find cos (5π/12) exactly. Solution:

Example Find tan 15 exactly. Solution: