How do you solve Sin^2 theta + cos theta = 2?

1 Answer
José F.
Apr 14, 2016

No solution.

Explanation:

The maximum value of sin^2theta is 1 and the maximum value of
costheta is also 1. Since both functions cannot be 1 at the same time, the problem has no solution.

However, if you want to try, let's see:

sin^2theta=1-cos^2theta

So the expression transforms into:

1-cos^2theta+costheta=2

cos^2theta-costheta+1=0
(This is an expression o the type ax^2+bx +c)

costheta=(1+-sqrt(1-4*1*1))/2

costheta=(1+-sqrt(-3))/2

There is no solution.

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