Sum and Difference Identities Part 2.

Last Friday, November 5, we learned more about sum and difference identities in different ways. This includes finding the coordinates of and the quadrant where it lies, verifying, finding exact values and expressing the following as function of .

EXAMPLE 1:


Step 1 : To figure out the points and we must identify the other point of the right triangle using the Pythagorean Thereom equation . Since is then...


In this case, the other point will equal to -15.



So the values will be...


Step 2: We must do the same step to figure out the values of and by using = . Since equals to then...

In this case, the other point will equal to -4.


So the values will be...



Now that we have all the values that we need to solve

Step 3 : We must solve for first. To do so, we must figure out the equation, which is...


Now all you have to do is plug in the values that equivalents the equation, like this...

Then multiply...

Which equals to...

So =

Step 4 : Now, we have to solve for . The equation for it is...


All we have to do now is plug in the values like the one we did from the previous equation, like this...

Then multiply...

Which equals to...

So =



The Quadrant in which it lies is in QII because cos = negative and sin = positive.