# Precalculus : Fundamental Trigonometric Identities

## Example Questions

### Example Question #21 : Fundamental Trigonometric Identities

Find the exact value

.

Explanation:

By the double angle formula

### Example Question #22 : Fundamental Trigonometric Identities

Find the exact value

.

Explanation:

By the double angle formula

### Example Question #23 : Fundamental Trigonometric Identities

Find the exact value

.

Explanation:

By the double-angula formula for cosine

For this problem

### Example Question #24 : Fundamental 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 #25 : Fundamental Trigonometric 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 #26 : Fundamental Trigonometric 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 #27 : Fundamental Trigonometric Identities

Compute

Explanation:

A useful trigonometric identity to remember for this problem is

or equivalently,

If we substitute  for , we get

### Example Question #28 : Fundamental Trigonometric Identities

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 #29 : Fundamental Trigonometric Identities

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

Explanation:

Write the half angle identity for sine.

Since we are given , the angle is equal to .  Set these two angles equal to each other and solve for .

Substitute this value into the formula.

### Example Question #30 : Fundamental Trigonometric Identities

Let  and  two reals. Given that:

What is the value of:

?

Explanation:

We have:

and :

(1)-(2) gives:

Knowing from the above formula that:( take a=b in the formula above)

This gives: