SOLUTION: Solve sin^2θ − 5cosθ = 5 for 0°≤θ≤360°

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Question 1042505: Solve sin^2θ − 5cosθ = 5 for 0°≤θ≤360°
Answer by ikleyn(52864) About Me  (Show Source):
You can put this solution on YOUR website!
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Solve sin^2(theta) - 5cos(theta) = 5 for 0° <= theta < 360°.
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Replace sin%5E2%28theta%29 by 1+-+cos%5E2%28theta%29 to have the equation for cos%28theta%29 only. You will get

1-cos%5E2%28theta%29+-+5cos%28theta%29 = 5,  or

cos%5E2%28theta%29+%2B+5cos%28theta%29+%2B+4 = 0.

Factor left side:

%28cos%28theta%29%2B4%29%2A%28cos%28theta%29+%2B1%29 = 0.

Then the equation deploys in two equations:

1)  cos%28theta%29+%2B+4 = 0,  or  cos%28theta%29 = -4,  which has no solutions,  and

2)  cos%28theta%29+%2B+1 = 0,  or  cos%28theta%29 = -1,  which has the solution theta = 180°.

Answer.  The solution is theta = 180°.