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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: ?
Â
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.
Â
We begin by considering our formula for the sum of two sines
Â
Â
Â
We will let and
 and plug these values into our formula.
Â
Â
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.
Â
We begin by considering the formula for the differences of two cosines.
Â
We will let   and Â
. Proceed by plugging these values into the formula.
Â
Â
Example Question #2 : Sum And Difference Of Sines And Cosines
Which of the following completes the identity
Â
Â
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:
Â
Â
To solve this problem we must use the identity
.  We will let
 and Â
.
Â
Â
Â
Â
Â
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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
TrueÂ
False
This answer is false.  is not the same as
.
For example, say  and
Â
Â
Â
Â
And so the correct identity to use for this is
Â
Example Question #7 : Sum And Difference Of Sines And Cosines
Solve for the following using the correct identity:
The correct identity to use for this kind of problem is
. We will let
  and Â
.
Â
Â
Example Question #3 : Sum And Difference Of Sines And Cosines
Which of the following is the correct to complete the following identity: Â ___?
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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