SOLUTION: Find, to the nearest degree, the roots of cos2&#952;-2cos&#952;=0 on the interval 0<&#952;<360

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Question 972252: Find, to the nearest degree, the roots of cos2θ-2cosθ=0 on the interval 0<θ<360
Answer by lwsshak3(11628) About Me  (Show Source):
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Find, to the nearest degree, the roots of cos2θ-2cosθ=0 on the interval 0<θ<360
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cos2θ-2cosθ=0
cos^2(θ)-sin^2(θ)-2cos(θ)
cos^2(θ)-1+cos^2(θ)-2cos(θ)=0
2cos^2(θ)-2cosθ-1=0
solve for cosθ by quadratic formula:
cos%28theta%29+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=2, b=-2, c=-1
cosθ=1.336 (reject, (-1 < cosx < 1)
or
cosθ=-0.366
θ=111.469˚, 248.13˚