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
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.