Precalculus : Sum and Difference Identities For Sine

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #2 : Sum And Difference Identities

Find  using the sum identity.

Possible Answers:

Correct answer:

Explanation:

Using the sum formula for sine,

where, 

yeilds:

.

Example Question #6 : Trigonometric Identities

Calculate .

Possible Answers:

Correct answer:

Explanation:

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

where

.

Therefore the result is as follows:

 

Example Question #2 : Sum And Difference Identities For Sine

Find the exact value for:  

Possible Answers:

Correct answer:

Explanation:

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 #3 : Sum And Difference Identities For Sine

Find the exact value of:   

Possible Answers:

Correct answer:

Explanation:

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 #4 : Sum And Difference Identities For Sine

In the problem below, and .

Find

.

Possible Answers:

Correct answer:

Explanation:

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 #5 : Sum And Difference Identities For Sine

In the problem below, and .

Find

.

Possible Answers:

Correct answer:

Explanation:

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 #1 : Sum And Difference Identities For Sine

Evaluate

.

Possible Answers:

Correct answer:

Explanation:

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 #2 : Sum And Difference Identities For Sine

Evaluate

.

Possible Answers:

Correct answer:

Explanation:

The angle  or .

Using the first one: 

We can find these values in the unit circle:

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