Question

Todd belives that `180^circ` and `270^circ` are solutions to the equations `5cos^2theta=-4costheta`. Show how you would check to determine whether Todd's solutions are correct?

Answer 1

See below.

Explanation:

In order to determine if Todd is right, we must solve for `theta`

`5cos^2theta=-4costheta`

Divide both sides by `costheta`

`5costheta=-4`

Divide both sides by `5`

`costheta=-4/5`

We know now that Todd is wrong. This is because we know that `cos180=-1` and `cos270=0`. Therefore, neither of these can be the solution to the equation.

One correct solution is `theta=143.13^circ`

graph{cosx [0, 10, -2.5, 2.5]}