copyright © 2011 pearson, inc. warm up what is the pythagorean identity?
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Copyright © 2011 Pearson, Inc.
Warm Up
What is the Pythagorean Identity?
Copyright © 2011 Pearson, Inc.
5.4Multiple
Angle Identities
Goal: Apply the double-angle identities.
Copyright © 2011 Pearson, Inc. Slide 5.4 - 3
What you’ll learn about
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 - 4
Double Angle Identities
sin2u 2sinu cosu
cos2u
cos2 u sin2 u
2cos2 u 1
1 2sin2 u
tan2u 2 tanu
1 tan2 u
Copyright © 2011 Pearson, Inc.
Proving a Double-Angle Identity
Prove.
Slide 5.4 - 5
Copyright © 2011 Pearson, Inc.
Proving a Double-Angle Identity
Slide 5.4 - 6
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When α = 30°, verify the identity for sin 2α.
Copyright © 2011 Pearson, Inc.
#1 Rewrite in a simpler form.
Copyright © 2011 Pearson, Inc.
#2 Rewrite in a simpler form.
Copyright © 2011 Pearson, Inc.
#3 Rewrite in a simpler form.
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#4 Rewrite in a simpler form.
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#5 Rewrite in a simpler form.
Copyright © 2011 Pearson, Inc.
#6 Rewrite in a simpler form.
Copyright © 2011 Pearson, Inc.
#7 Evaluate without a calculator.
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#8 Evaluate without a calculator.
Copyright © 2011 Pearson, Inc. Slide 5.4 - 16
Half-Angle Identities
sinu
2
1 cosu
2
cosu
2
1 cosu
2
tanu
2
1 cosu
1 cosu1 cosu
sinusinu
1 cosu
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