11-4 Sum and Difference Identities Warm Up Find each product, if possible.

1. AB

Holt McDougal Algebra 2

2. BA

11-4 Sum and Difference Identities

Objectives

Evaluate trigonometric expressions by using sum and difference identities.

Use matrix multiplication with sum and difference identities to perform rotations.

Holt McDougal Algebra 2

11-4 Sum and Difference Identities

Vocabulary

rotation matrix

Holt McDougal Algebra 2

11-4 Sum and Difference Identities

Matrix multiplication and sum and difference identities are tools to find the coordinates of points rotated about the origin on a plane.

Holt McDougal Algebra 2

11-4 Sum and Difference Identities Holt McDougal Algebra 2

11-4 Sum and Difference Identities Holt McDougal Algebra 2

11-4 Sum and Difference Identities Example 1A: Evaluating Expressions with Sum and Difference Identities Find the exact value of cos 15 ° .

cos 15 ° = cos ( 45 ° – 30 ° )

Write 15 ° as the difference 45 ° – 30° because trigonometric values of 45 ° and 30° are known.

= cos 45 ° cos 30 °

Apply the identity for cos (A – B).

+ sin 45 ° sin 30 °

Evaluate.

Simplify.

Holt McDougal Algebra 2