Trigonometry : Sum and Difference of Sines and Cosines

Study concepts, example questions & explanations for Trigonometry

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Example Questions

Example Question #1 : Sum And Difference Of Sines And Cosines

What is the correct formula for the sum of two sines: ?

 

Possible Answers:

Correct answer:

Explanation:

This is a known trigonometry identity.  Whenever you are adding two sine functions, you can plug  and  into the formula to solve for this sum

Example Question #2 : Sum And Difference Of Sines And Cosines

Solve for the following given that .  Use the formula for the sum of two sines.

 

Possible Answers:

Correct answer:

Explanation:

We begin by considering our formula for the sum of two sines

 

 

 

We will let and  and plug these values into our formula.

 

 

Example Question #3 : Sum And Difference Of Sines And Cosines

Solve for the following using the formula for the differences of two cosines.  Do not simplify.

 

Possible Answers:

Correct answer:

Explanation:

We begin by considering the formula for the differences of two cosines.

 

We will let    and  .  Proceed by plugging these values into the formula.

 

 

Example Question #4 : Sum And Difference Of Sines And Cosines

Which of the following completes the identity

 

 

Possible Answers:

Correct answer:

Explanation:

This is a known trigonometry identity and has been proven to be true.  It is often helpful to solve for the quantity within a cosine function when there are unknowns or if the quantity needs to be simplified

Example Question #5 : Sum And Difference Of Sines And Cosines

Solve for the following using the correct identity:

 

 

Possible Answers:

Correct answer:

Explanation:

To solve this problem we must use the identity

.  We will let  and  .

 

 

 

 

 

 

Example Question #6 : Sum And Difference Of Sines And Cosines

True or False: To solve for a problem in the form of , I use the identity .

Possible Answers:

False

True 

Correct answer:

False

Explanation:

This answer is false.   is not the same as .

For example, say  and

 

 

 

 

And so the correct identity to use for this is

 

Example Question #7 : Sum And Difference Of Sines And Cosines

Solve for the following using the correct identity:

Possible Answers:

Correct answer:

Explanation:

The correct identity to use for this kind of problem is

We will let   and   .

 

 

Example Question #8 : Sum And Difference Of Sines And Cosines

Which of the following is the correct to complete the following identity:  ___?

Possible Answers:

Correct answer:

Explanation:

This is a known trigonometry identity and has been proven to be true.  It is often helpful to solve for the quantity within a cosine function when there are unknowns or if the quantity needs to be simplified

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