# Precalculus : Trigonometric Identities

## Example Questions

### Example Question #4 : Use Product/Sum Identities To Express A Product As A Sum Or Difference

Which expression is equivalent to

?

Explanation:

The relevant trigonometric identity is

In this case, "u" is and "v" is .

.

### Example Question #1 : Double And Half Angle Identities

Find the exact value

.

Explanation:

By the double angle formula

### Example Question #1 : Double Angle Identities

Find the exact value

.

Explanation:

By the double angle formula

### Example Question #3 : Double And Half Angle Identities

Find the exact value

.

Explanation:

By the double-angula formula for cosine

For this problem

### Example Question #41 : Trigonometric Identities

Find the exact value

.

Explanation:

By the double-angle formula for the sine function

we have

thus the double angle formula becomes,

### Example Question #1 : Double Angle Identities

If , which of the following best represents ?

Explanation:

The expression  is a double angle identity that can also be rewritten as:

Replace the value of theta for .

### Example Question #6 : Double And Half Angle Identities

Which expression is equivalent to  ?

Explanation:

The relevant trigonometric identity is:

In this case, "u" is since .

The only one that actually follows this is

### Example Question #1 : Double And Half Angle Identities

Compute

Explanation:

A useful trigonometric identity to remember for this problem is

or equivalently,

If we substitute  for , we get

### Example Question #251 : Pre Calculus

Compute

Explanation:

A useful trigonometric identity to remember is

If we plug in  into this equation, we get

We can divide the equation by 2 to get

### Example Question #9 : Double And Half Angle Identities

Using the half-angle identities, which of the following answers best resembles ?