Question 685120: Given that sin(3θ)= (1/5) and (π/2)<3θ<π: Find cos(3θ), sin(6θ), and tan (3θ/2)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Given that sin(3θ)= (1/5) and (π/2)<3θ<π: Find cos(3θ), sin(6θ), and tan (3θ/2)
You are working with reference angle 3θ in quadrant II where sin>0, cos<0, and tan<0
sin3θ=opposite side/hypotenuse=1/5
adjacent side=√(5^2-1^2)=√(25-1)=√24
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cos(3θ)=-√24/5
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Identity: sin 2s=2sins cos s
sin(6θ)=2sin3θcos3θ
=2*1/5*-√24/5
=-(2√24)/25
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Identity: tan s/2= (sin s)/(1+cos s)
tan (3θ/2)=sin3θ/1+cos3θ
=(1/5)/(1-√24/5)
=(1/5)/(5-√24)/5
=1/(5-√24)
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