Warm Up n What is the Pythagorean Identity

Warm Up n What is the Pythagorean Identity? Copyright © 2011 Pearson, Inc.

Goal: Apply the double-angle identities. 5. 4 Multiple Angle Identities Copyright © 2011 Pearson, Inc.

What you’ll learn about n n Double-Angle Identities Power-Reducing Identities Half-Angle Identities Solving Trigonometric Equations … and why These identities are useful in calculus courses. Copyright © 2011 Pearson, Inc. Slide 5. 4 - 3

Double Angle Identities Copyright © 2011 Pearson, Inc. Slide 5. 4 - 4

Proving a Double-Angle Identity Prove. Copyright © 2011 Pearson, Inc. Slide 5. 4 - 5

Proving a Double-Angle Identity n Copyright © 2011 Pearson, Inc. Slide 5. 4 - 6

When α = 30°, verify the identity for sin 2α. Copyright © 2011 Pearson, Inc.

#1 Copyright © 2011 Pearson, Inc. Rewrite in a simpler form.

#2 Copyright © 2011 Pearson, Inc. Rewrite in a simpler form.

#3 Copyright © 2011 Pearson, Inc. Rewrite in a simpler form.

#4 Copyright © 2011 Pearson, Inc. Rewrite in a simpler form.

#5 Rewrite in a simpler form. Copyright © 2011 Pearson, Inc.

#6 Copyright © 2011 Pearson, Inc. Rewrite in a simpler form.

#7 Evaluate without a calculator. Copyright © 2011 Pearson, Inc.

#8 Evaluate without a calculator. Copyright © 2011 Pearson, Inc.

Half-Angle Identities Copyright © 2011 Pearson, Inc. Slide 5. 4 - 16