How do you solve trigonometric equations by the quadratic formula?
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
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".)
Now we need to solve
That's going to be a problem because
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: