### All Precalculus Resources

## Example Questions

### Example Question #23 : Trigonometric Identities

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 #24 : Trigonometric Identities

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:

### Example Question #25 : Trigonometric Identities

Find using the sum identity.

**Possible Answers:**

**Correct answer:**

Using the sum formula for sine,

where,

,

yeilds:

.

### Example Question #26 : Trigonometric Identities

Calculate .

**Possible Answers:**

**Correct answer:**

Notice that is equivalent to . With this conversion, the sum formula can be applied using,

where

, .

Therefore the result is as follows:

.

### Example Question #27 : Trigonometric Identities

Find the exact value for:

**Possible Answers:**

**Correct answer:**

In order to solve this question, it is necessary to know the sine difference identity.

The values of and must be a special angle, and their difference must be 15 degrees.

A possibility of their values that match the criteria are:

Substitute the values into the formula and solve.

Evaluate .

### Example Question #28 : Trigonometric Identities

Find the exact value of:

**Possible Answers:**

**Correct answer:**

In order to find the exact value of , the sum identity of sine must be used. Write the formula.

The only possibilites of and are 45 and 60 degrees interchangably. Substitute these values into the equation and evaluate.

### Example Question #29 : Trigonometric Identities

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 sine sum formula, we see:

### Example Question #30 : Trigonometric Identities

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 sine difference formula, we see:

### Example Question #11 : Sum And Difference Identities

Evaluate

.

**Possible Answers:**

**Correct answer:**

is equivalent to or more simplified .

We can use the sum identity to evaluate this sine:

From the unit circle, we can determine these measures:

### Example Question #32 : Trigonometric Identities

Evaluate

.

**Possible Answers:**

**Correct answer:**

The angle or .

Using the first one:

We can find these values in the unit circle:

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