# Trigonometry : Quadratic Formula with Trigonometry

## Example Questions

### Example Question #247 : Trigonometry

Which is not a solution for for  ?

Explanation:

or

Solve for :

Explanation:

### Example Question #61 : Solving Trigonometric Equations

Find the roots for

No solution

No solution

Explanation:

To solve, use the quadratic formula:

Both and are outside of the range of the sine function, so there is no solution.

### Example Question #62 : Solving Trigonometric Equations

Solve for :

Explanation:

, outside the range for cosine.

according to a calculator.

The other angle with a cosine of 0.78 would be .

### Example Question #21 : Quadratic Formula With Trigonometry

Solve for :

Explanation:

5 is outside the range for cosine, so the only solution that works is :

according to a calculator

The other angle with a cosine of is

### Example Question #64 : Solving Trigonometric Equations

Solve for :

Explanation:

-2 is outside the range of cosine, so the answer has to come from :

according to a calculator

The other angle with a cosine of is

### Example Question #61 : Solving Trigonometric Equations

Solve the equation

for .

Explanation:

First of all, we can use the Pythagorean identity  to rewrite the given equation in terms of .

This is a quadratic equation in terms of ; hence, we can use the quadratic formula to solve this equation for .

where .

.

Now,  when , and  when  or .

Hence, the solutions to the original equation  are

### Example Question #61 : Solving Trigonometric Equations

In the interval , what values of x satisfy the following equation?

Explanation:

We start by rewriting the  term on the right hand side in terms of .

We then move everything to the left hand side of the equation and cancel.