SOLUTION: Could you please show me out to work out how many solutions there are to sinθ + 2cosθ = 0 on interval -π ≤ θ ≤ π/2 ? I'm really having a proble
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Question 729193: Could you please show me out to work out how many solutions there are to sinθ + 2cosθ = 0 on interval -π ≤ θ ≤ π/2 ? I'm really having a problem with it. I know 2cosθ doesn't equal cos2θ.. but I'm thinking that there might be some unusual exception, because if it did that would make this problem work out perfectly. Thank you!! :) Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! sinθ + 2cosθ = 0
sinθ=-2cosθ
square both sides
sin^2θ=4cos^2θ=4(1-sin^2θ)=4-4sin^2θ
sin^2θ=4-4sin^2θ
5sin^2θ=4
sin^2θ=4/5
take sqrt of both sides
sinθ=2/√5
θ≈2.034 (in quadrant II where sin>0)
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