5.4a.notebook
February 28, 2012
DOUBLE ANGLE FORMULAS
1. sin 2A = sin(A + A) *use sum formula
sinAcosB + cosAsinB
Find the exact value of cos 75o using the sum and difference formulas.
sinAcosA +cos AsinA
2sinAcosA
ex. sin 2(π/4) = 2sin45cos45 = ex. sin70 = 2sin35cos35
3. tan2A = 2tanA or sin2A
1­tan2A cos2A
ex. Find the exact value of cos275 ­sin275.
2. cos2A = cos(A+A)
cosAcosB­sinAsinB
= cosAcosA­sinAsinA
= cos2A ­ sin2A
=(1­sin2A) ­ sin2A
=1­2sin2A
=cos2A ­ (1­cos2A)
=2cos2A ­ 1
sin2A + cos2A = 1
sin2A = 1 ­ cos2A cos2A= 1 ­ sin2A
ex. Find the exact value of 2sin75cos75.
ex. Find the exact value of tan 150.
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5.4a.notebook
Prove: cos4θ­sin4θ = cos2θ
Prove: sin8x = 2sin4xcos4x
February 28, 2012
Prove: sin3x = sinx(3­4sin2x)
Prove: cos4x = 2(2cos2x­1)2 ­ 1 Half Angle Formulas
Journal: Write an expression equivalent to
1­2sin215o. What is the exact value?
Find the exact value of cos 15.
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