### All Precalculus Resources

## Example Questions

### Example Question #4 : Product/Sum Identities

Evaluate the following.

**Possible Answers:**

**Correct answer:**

Here we use the double angle identity for sine, which is

.

We can rewrite the originial expression as using the double angle identity.

From here we can calculate that

.

### Example Question #5 : Product/Sum Identities

Evaluate the following expression.

**Possible Answers:**

**Correct answer:**

One of the double angle formuals for cosine is

.

We can use this double angle formula for cosine to rewrite the expression given as the because and .

We can then calculate that

.

### Example Question #1 : Product/Sum Identities

Evaluate the following.

**Possible Answers:**

**Correct answer:**

Here we can use another double angle formula for cosine,

.

Here , and so we can use the double angle formula for cosine to rewrite the expression as

.

From here we just recognize that

.

### Example Question #231 : Pre Calculus

Evaluate the following expression.

**Possible Answers:**

**Correct answer:**

Here we can use yet another double angle formula for cosine:

.

First, realize that .

Next, plug this in to the double angle formula to find that

.

Here we recognize that

### Example Question #31 : Trigonometric Identities

Simplify the following. Leave your answer in terms of a trigonometric function.

**Possible Answers:**

**Correct answer:**

This is a quick test of being able to recall the angle sum formula for sine.

Since,

, and here

, we can rewrite the expression as

.

### Example Question #9 : Product/Sum Identities

Which of the following expressions best represent ?

**Possible Answers:**

**Correct answer:**

Write the trigonometric product and sum identity for .

For , replace with and simplify the expression.

### Example Question #10 : Product/Sum Identities

Find the exact answer of:

**Possible Answers:**

**Correct answer:**

The product and sum formula can be used to solve this question.

Write the formula for cosine identity.

Split up into two separate cosine expressions.

Substitute the 2 known angles into the formula and simplify.

### Example Question #1 : Use Product/Sum Identities To Express A Product As A Sum Or Difference

Simplify the following. Leave your answer in terms of a trigonometric function.

**Possible Answers:**

**Correct answer:**

This is a simple exercise to recognize the half angle formula for cosine.

The half angle formula for cosine is

.

In the expression given .

With this in mind we can rewrite the expression as the , or, after dividing by two,

### Example Question #1 : Use Product/Sum Identities To Express A Product As A Sum Or Difference

Solve the following over the domain to .

**Possible Answers:**

**Correct answer:**

Here we can rewrite the left side of the equation as because of the double angle formula for sin, which is .

Now our equation is

,

and in order to get solve for we take the of both sides. Just divide by two from there to find .

The only thing to keep in mind here is that the period of the function is half of what it normally is, which is why we have to solve for and then add to each answer.

### Example Question #31 : Trigonometric Identities

Solve over the domain to .

**Possible Answers:**

**Correct answer:**

We can rewrite the left side of the equation using the angle difference formula for cosine

as

.

From here we just take the of both sides and then add to get .

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