SOLUTION: If 8tan(theta) = 3cos(theta) , find the value of sin(theta)

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Question 972530: If 8tan(theta) = 3cos(theta) , find the value of sin(theta)
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
If 8tan(theta) = 3cos(theta) , find the value of sin(theta)
***
theta=x=acute angle
8tanx=3cosx
%288sinx%2Fcosx%29=%283cosx%29
8sinx=3cos^2(x)
8sinx=3(1-sin^2(x))
8sinx=3-3sin^2(x)
3sin^2(x)+8sinx-3=0
(sinx+3)(3sinx-1)=0
..
sinx+3=0
sinx=-3 (reject, (-1 ≤ sinx ≤ 1))
or
3sinx-1=0
sinx=1/3
x≈19.47˚