Question 825816
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
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a)sin2x=2sinxcosx=2*4/5*3/5=24/25
cos2x=&#8730;(1-sin^2(2x))=&#8730;(1-(576/625))=&#8730;(1-(576/625))=&#8730;(49/625)=7/25
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b)sin4x=2sin2xcos2x=2*24/25*7/25=336/625
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calculator check:
cosx=4/5
x&#8776;36.87&#730;
4x&#8776;147.48&#730;
sin4x&#8776;sin(147.48&#730;)&#8776;0.5376..
exact value as calculated=336/625&#8776;0.5376..