SOLUTION: If x+4=3sin(&#952;) for 0<&#952;<&#960;/2 express cos(2&#952;) in terms of x. cos(2&#952;)=

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Question 865410: If x+4=3sin(θ) for 0<θ<π/2 express cos(2θ) in terms of x.
cos(2θ)=
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
If x+4=3sin(θ) for 0<θ<π/2 express cos(2θ) in terms of x.
cos(2θ)=
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cos(2θ)==cos^2(θ)-sin^2(θ)
..
x+4=3sin(θ)
sin(θ)=(x+4)/3
sin^2(θ)=(x+4)^2/9
cos^2(θ)=1-sin^2(θ)=1-(x+4)^2/9=(9-(x+4)^2)/9
cos(2θ)=(9-(x+4)^2)/9-(x+4)^2/9
cos(2θ=(9-2(x+4)^2)/9=9-2(x^2+8x+16)/9=(9-2x^2-16x-32)/9=(-2x^2-16x-23)/9
cos(2θ=-(2x^2+16x+23)/9