SOLUTION: Need help solving the trigonometric equation sin2theta + square root 2 cos theta=0

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Question 496428: Need help solving the trigonometric equation sin2theta + square root 2 cos theta=0
Answer by lwsshak3(11628) About Me  (Show Source):
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sin2theta + square root 2 cos theta=0
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for 0 ≤ x ≤ 2π
sin2x +√2 cosx=0
2sinxcosx+√2cosx=0
cosx(2sinx+√2)=0
..
cosx=0
x=π/2 and 3π/2
..
2sinx+√2)=0
2sinx=-√2)
sinx=-√2/2
x=5π/4 and 7π/4 (in quadrants III and IV where sin<0)
ans:
x=π/2, 3π/2, 5π/4, and 7π/4