Warm­up:
Verify.
cos3xsin2x = (sin2x ­ sin4x)cos x
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Section 5.5:
Double Angle and
Power Reducing
Formulas
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More Trigonometric Identities:
Double Angle Formulas:
sin(2u) = 2sinucosu
cos(2u)= cos2u - sin2u
= 2cos2u - 1
= 1 - 2sin2u
tan(2u)=
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Examples using double­angle formulas.
1. Find all solutions of 2cos x + sin 2x = 0.
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2. Use a double­angle formula to rewrite the equation
sin 4x = ­2sin 2x Then find the values from [0, 2π)
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3. Use a double­angle formula to rewrite the equation
cos x + cos 2x = ­ 1 Then find the values from [0, 2π)
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4. Use the following to find sin 2x, cos 2x, and tan 2x.
cos x = 5 , 3π < x < 2π
13 2
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*There are also Power Reducing, Half-Angle,
Product-to-Sum, and Sum-to-Product formulas that
you can find on pages 416-418 in your book.
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Classwork/Homework:
pg. 418
#s 3-8,9,10,12,13,14
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