# Trigonometry : Sum and Difference of Sines and Cosines

## Example Questions

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

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

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.

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.

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

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:

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 .

False

True

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:

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:  ___?