### All Trigonometry Resources

## Example Questions

### Example Question #1 : Sum, Difference, And Product Identities

True or false:

.

**Possible Answers:**

False

True

Cannot be determined

**Correct answer:**

False

The sum of sines is given by the formula .

### Example Question #2 : Sum, Difference, And Product Identities

True or false: .

**Possible Answers:**

False

True

Cannot be determined

**Correct answer:**

False

The difference of sines is given by the formula .

### Example Question #1 : Complete A Proof Using Sums, Differences, Or Products Of Sines And Cosines

True or false: .

**Possible Answers:**

Cannot be determined

False

True

**Correct answer:**

False

The sum of cosines is given by the formula .

### Example Question #2 : Complete A Proof Using Sums, Differences, Or Products Of Sines And Cosines

True or false: .

**Possible Answers:**

Cannot be determined

True

False

**Correct answer:**

False

The difference of cosines is given by the formula .

### Example Question #5 : Sum, Difference, And Product Identities

Which of the following correctly demonstrates the compound angle formula?

**Possible Answers:**

**Correct answer:**

The compound angle formula for sines states that .

### Example Question #6 : Sum, Difference, And Product Identities

Which of the following correctly demonstrates the compound angle formula?

**Possible Answers:**

**Correct answer:**

The compound angle formula for cosines states that .

### Example Question #7 : Sum, Difference, And Product Identities

Simplify by applying the compound angle formula:

**Possible Answers:**

**Correct answer:**

Using the compound angle formula, we can rewrite each half of the non-coefficient terms in the given expression. Given that and , substitution yields the following:

This is the formula for the product of sine and cosine, .

### Example Question #8 : Sum, Difference, And Product Identities

Simplify by applying the compound angle formula:

**Possible Answers:**

**Correct answer:**

Using the compound angle formula, we can rewrite each half of the non-coefficient terms in the given expression. Given that and , substitution yields the following:

This is the formula for the product of two cosines, .

### Example Question #9 : Sum, Difference, And Product Identities

Using and the formula for the sum of two sines, rewrite the sum of cosine and sine:

**Possible Answers:**

**Correct answer:**

Substitute for :

Apply the formula for the sum of two sines, :

### Example Question #10 : Sum, Difference, And Product Identities

Using and the formula for the difference of two sines, rewrite the difference of cosine and sine:

**Possible Answers:**

**Correct answer:**

Substitute for :

Apply the formula for the difference of two sines, .

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