SOLUTION: Use trigonometric identities to solve 2cos2(&#952;)=sin(&#952;)+1 exactly for 0&#8804;&#952;<2&#960;. If there is more than one answer, enter your answers as a comma separated list

Algebra ->  Trigonometry-basics -> SOLUTION: Use trigonometric identities to solve 2cos2(&#952;)=sin(&#952;)+1 exactly for 0&#8804;&#952;<2&#960;. If there is more than one answer, enter your answers as a comma separated list      Log On


   

Question 865407: Use trigonometric identities to solve 2cos2(θ)=sin(θ)+1 exactly for 0≤θ<2π. If there is more than one answer, enter your answers as a comma separated list
Answer by lwsshak3(11628) About Me  (Show Source):
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Use trigonometric identities to solve 2cos2(θ)=sin(θ)+1 exactly for 0≤θ<2π. If there is more than one answer, enter your answers as a comma separated list.
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2cos%5E2%28theta%29=sin%28theta%29%2B1
2%281-sin%5E2%28theta%29%29=sin%28theta%29%2B1
2-2sin%5E2%28theta%29=sin%28theta%29%2B1
2sin%5E2%28theta%29%2Bsin%28theta%29-1=0
%282sin%28theta%29-1%29+%28sin%28theta%29%2B1%29
..
2sinθ-1=0
sinθ=1/2
θ=π/6, 5π/6
..
sinθ+1=0
sinθ=-1
θ=3π/2
..
θ=π/6, 5π/6, 3π/2