# How do you solve trigonometric equations by the quadratic formula?

##### 1 Answer

The quadratic formula can be useful in solving trigonometric (or other) kinds of equation. But strictly speaking, the quadratic formula is used only to solve quadratic equations.

Here is an example:

We can use the quadratic formula to solve

We get

Now what if we needed to solve:

This is not a quadratic equation.

But, if we substitute

But we want

And (taking 3rd roots on both sides) gives us

Now, suppose we need to solve

This is a trigonometric equation, not a quadratic equation. Or is it?

Can't we "turn it into" a quadratic by substituting? (Such equations are sometimes called "quadratic in form".)

Let

So

Now we need to solve

That's going to be a problem because

Solve

In this case there is a solution, but it is not one of the special angles. Using tables or electronics, we can get the reference angle

In degrees the solutions are: