### All Precalculus Resources

## Example Questions

### Example Question #1 : Sum And Difference Identities For Cosine

Evaluate the exact value of:

**Possible Answers:**

**Correct answer:**

In order to solve , two special angles will need to be used to solve for the exact values.

The angles chosen are and degrees, since:

Write the formula for the cosine additive identity.

Substitute the known variables.

### Example Question #2 : Sum And Difference Identities For Cosine

Find the exact value of .

**Possible Answers:**

**Correct answer:**

To solve , we will need to use both the sum and difference identities for cosine.

Write the formula for these identities.

To solve for and , find two special angles whose difference and sum equals to the angle 15 and 75, respectively. The two special angles are 45 and 30.

Substitute the special angles in the formula.

Evaluate both conditions.

Solve for .

### Example Question #3 : Sum And Difference Identities For Cosine

In the problem below, and .

Find

.

**Possible Answers:**

**Correct answer:**

Since and is in quadrant I, we can say that and and therefore:

.

So .

Since and is in quadrant I, we can say that and and therefore:

. So .

Using the cosine sum formula, we then see:

.

### Example Question #4 : Sum And Difference Identities For Cosine

In the problem below, and .

Find

.

**Possible Answers:**

**Correct answer:**

Since and is in quadrant I, we can say that and and therefore:

.

So .

Since and is in quadrant I, we can say that and and therefore:

.

So .

Using the cosine difference formula, we see: