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Trigonometry question?

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when solving for 0 < θ< or = 360
2tan( θ)= cos (θ)

so i want to see if my logic to solving is correct!
i found the angles are 90 and 270

asked Mar 11, 2013 in TRIGONOMETRY by anonymous Apprentice

1 Answer

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The equation is 2tan( θ)= cos (θ)

Recall the trignometric quotient rule:tanθ=sinθ/cosθ

2sinθ/cosθ=cosθ

Simplify

2sinθ=cos^2θ

Recall the trignometric pythagora's rule:cos^2θ=1-sin^2θ

2sinθ=1-sin^2θ

sin^2θ+2sinθ-1=0

sinθ=-2+√4-(-4)/2

        =(-2+√8) /2

        =-1+√2

θ=24.456,155.544,

answered Mar 11, 2013 by bradely Mentor

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