February 03, 2010

5.4 Multiple Angle Formulas

Double Angle Formulas

sin 2u = 2 sin u cos u

cos 2u = cos2u - sin2u

= 2cos2u - 1

= 1 - 2sin2u

tan 2u = 2 tan u1 - tan2u

February 03, 2010

1. Use the sum and difference formulas to prove the identity.

sin 2u = 2 sin u cos u

February 03, 2010

2. Use the sum and difference formulas to prove the identity.

cos 2u = 2cos2u - 1

February 03, 2010

3. Find all solutions in the interval [0, 2 )

2 cos x + sin 2x = 0

February 03, 2010

4. Write the expression as one involving only sin x and cos x.

sin 2x + cos 2x

February 03, 2010

Prove the identity.

sin 3x = (sin x)(3 - 4 sin2 x)

6.

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February 03, 2010

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February 03, 2010

Power-Reducing Formulas

sin2u = 1 - cos 2u cos2u = 1 + cos 2u tan2u = 1 - cos 2u 2 2 1 + cos 2u

5. Rewrite sin4x as a sum of first powers of cosines and multiple angles.Rewrite sin4x as a sum of first powers of cosines and multiple angles.

6.

DAY 2

February 03, 2010

Half-Angle Identities

sin = u 1 - cos u2 2

+-

cos = +-

u 1 + cos u2 2

tan =u2

+-

+-

+-

1 - cos u1 + cos u

1 - cos u sin u

sin u1 + cos u

February 03, 2010

7. Using the half-angle formulas give the exact value of sin 105

February 03, 2010

Use the half-angle identities to find all solutions in the interval [0, 2π).

sin2 x = cos2 x2

8.