Precalculus : Sum and Difference Identities

Study concepts, example questions & explanations for Precalculus

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Example Questions

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Example Question #1 : Sum And Difference Identities

According to the trigonometric identities, 

Possible Answers:

Correct answer:

Explanation:

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:

Explanation:

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.

Explanation:

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

Correct answer:

No it is not an identity

Explanation:

Therefore, this is not an identity.

Example Question #4 : Sum And Difference Identities

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

Possible Answers:

Correct answer:

Explanation:

Using the identity, we can break up the 255 into and then solve:   

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.

Explanation:

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:

Explanation:

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

Is the following equation an identity?

Possible Answers:

The answer cannot be determined from the information provided.

No it is not an identity

Yes it is an identity

Correct answer:

No it is not an identity

Explanation:

Due to this inequality, this is not an identity.

Example Question #2 : Trigonometric Identities

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

Possible Answers:

Correct answer:

Explanation:

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

Example Question #1 : Sum And Difference Identities

Evaluate the exact value of:  

Possible Answers:

Correct answer:

Explanation:

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.

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