# Precalculus : Solve Trigonometric Equations and Inequalities

## Example Questions

### Example Question #1 : Solve Trigonometric Equations And Inequalities

Use trigonometric identities to solve the following equation for :

Explanation:

Use the trigonometric identities to switch sec into terms of tan:

hence,

So we have , making

Therefore the solution is  for n being any integer.

### Example Question #2 : Solve Trigonometric Equations And Inequalities

Which of the following is not a solution to   for

Explanation:

We begin by setting the right side of the equation equal to 0.

The equation might be easier to factor using the following substitution.

This gives the following

This can be factored as follows

Therefore

Replacing our substitution therefore gives

Within our designated domain, we get three answers between our two equations.

when

when

Therefore, the only choice that isn't correct is

### Example Question #3 : Solve Trigonometric Equations And Inequalities

Find one possible value of .

Explanation:

Begin by isolating the tangent side of the equation:

Next, take the inverse tangent of both sides:

Divide by five to get the final answer:

### Example Question #4 : Solve Trigonometric Equations And Inequalities

Use trigonometric identities to solve for the angle value.

Explanation:

There are two ways to solve this problem. The first involves two trigonometric identities:

The second method allows us to only use the first trigonometric identity:

### Example Question #5 : Solve Trigonometric Equations And Inequalities

Use trigonometric identities to solve the equation for the angle value.