Trigonometric functions can also show up in pseudo-quadratics - a quadratic where the variable being squared is not x but a trig function.

On exams, these equations often require using the Pythagorean identity sin2θ+cos2θ=1.

Example

Solve the equation 2cos2x=3sinx for 0≤x<2π.

We start by rewriting everything in terms of sin:

where u=sinx.

Now sinx=21​ when x=6π​ or 65π​, and sinx is never equal to −2.