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: ___?      