Simplifying a Trig Equation: Finding the Zeros

[physstudent1]

Homework Statement

(this is really only part of my problem it's an optimization problem but this is where I'm stuck)
Find the zeros of: cos^2(x)-sin^(x)+cos(x)

Homework Equations

The Attempt at a Solution

I've been trying to use trig identities such as sin^2 + cos^2 = 1 but it's not getting me anywhere I know the answer is pi/3 because our teacher told us but I can't seem to get it.

 

[EnumaElish]

I'd try to convert all the terms to cos(x), then set y = cos(x), then use the quadratic formula.

 

[physstudent1]

thanks I got 1/2 and -1 for the roots with that then set that equal to cos(x) to find the roots of the actual problem ?

 

[rocomath]

is this your problem?

\cos^{2}{x}-\sin{x}+\cos{x}

you have sin^x ... idk how to interpret that

 

[Astronuc]

Or is it

\cos^{2}{x}-\sin^{2}{x}+\cos{x} ??