Question 866179: Use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2π). (Enter your answers as a comma-separated list. Round your answers to three decimal places where appropriate.)
sin θ − cos θ = (1/5)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2π). (Enter your answers as a comma-separated list. Round your answers to three decimal places where appropriate.)
sin θ − cos θ = (1/5)
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use x in place of θ:
cosx=sinx-1/5
√(1-sin^2x)=sinx-1/5
square both sides:
1-sin^2x=sin^2x-(2/5)sinx+1/25
2sin^2x-(2/5)sinx-24/25=0
50sin^2x-10sinx-24=0
25sin^2x-5sinx-12=0
(5sinx+3)(5sinx-4)=0
sinx=-3/5
or
sinx=4/5
x=3.785, 5.639, 0.927, 2.214
note: don't know how to do it with double or half-angle formulas, but this is as good as any method.
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