SOLUTION: If cos(theta)=4/5, 0<(theta)<pi/2, find the exact value of a) Sin 2(theta) b) Sin 4(theta)

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Question 825816: If cos(theta)=4/5, 0<(theta) find the exact value of
a) Sin 2(theta)
b) Sin 4(theta)
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
If cos(theta)=4/5, 0<(theta) find the exact value of
a) Sin 2(theta)
b) Sin 4(theta)
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cosx=4/5 (working with a (3-4-5) reference right triangle)
sinx=3/4
..
a)sin2x=2sinxcosx=2*4/5*3/5=24/25
cos2x=√(1-sin^2(2x))=√(1-(576/625))=√(1-(576/625))=√(49/625)=7/25
..
b)sin4x=2sin2xcos2x=2*24/25*7/25=336/625
..
calculator check:
cosx=4/5
x≈36.87˚
4x≈147.48˚
sin4x≈sin(147.48˚)≈0.5376..
exact value as calculated=336/625≈0.5376..