### All Precalculus Resources

## Example Questions

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

According to the trigonometric identities,

**Possible Answers:**

**Correct answer:**

The trigonometric identity , is an important identity to memorize.

Some other identities that are important to know are:

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

Use the sum or difference identity to find the exact value:

**Possible Answers:**

**Correct answer:**

Again, here we break up the 165 into and solve using the sin identity:

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

Is the following equation an identity?

**Possible Answers:**

It cannot be determined from the given information.

No it is not an identity.

Yes it is an identity.

**Correct answer:**

No it is not an identity.

and so this is again not an identity

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

Is the following equation an identity? ?

**Possible Answers:**

Yes it is an identity

The question cannot be answered based on the information provided.

No it is not an identity

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

Use the sum or difference identity to find the exact value:

**Possible Answers:**

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

Is the following equation an identity?

**Possible Answers:**

It cannot be determined from the given information.

Yes it is an identity.

No it is not an identity.

**Correct answer:**

No it is not an identity.

and due to this inequality, this is not an identity

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

Use the sum or difference identity to find the exact value:

**Possible Answers:**

**Correct answer:**

Using the identity, we can break up the into and then solve: and so the correct answer is .

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

**Possible Answers:**

The answer cannot be determined from the information provided.

No it is not an identity

Yes it is an identity

### Example Question #2 : Trigonometric Identities

Use the sum or difference identity to find the exact value of .

**Correct answer:**

Here we break up the into and solve using the sin identity: and so here the credited answer is .

### Example Question #1 : Solving Trigonometric Equations And Inequalities

Use trigonometric identities to solve the following equation for :

**Possible Answers:**

**Correct answer:**

Use the trigonometric identities to switch sec into terms of tan:

hence,

So we have , making

Therefore the solution is for n being any integer.