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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