# Sum/Difference Identity

• Nov 15th 2009, 07:28 AM
saintv
Sum/Difference Identity
Here is the question word for word:

Given that sinA = 7/25, and cosB = 9/41 and neither P(A) nor P(B) are in quadrant 1, find:

(a) sin(A+B)

I know that my first step in order to do this is solve for the unknowns in order to use an identity to answer the question. When I do this, I get cosA = 24/25 and sinB = 40/41. I have no problem with this step.

It is when I look in my answer key and see that cosA = - 24/25 and sinB = -40/41 that I am confused: why are they negative?

Here's what I already know:

• Cosine is postive in quadrants 1 & 4
• Sin is postive in quadrants 1 & 2
• Tan is postive in quadrants 1 & 3
• Neither point A or point B are in quadrant 1

Still, I don't understand why its negative, I'm having a brain block here.
• Nov 15th 2009, 07:43 AM
Quote:

Originally Posted by saintv
Here is the question word for word:

Given that sinA = 7/25, and cosB = 9/41 and neither P(A) nor P(B) are in quadrant 1, find:

(a) sin(A+B)

I know that my first step in order to do this is solve for the unknowns in order to use an identity to answer the question. When I do this, I get cosA = 24/25 and sinB = 40/41. I have no problem with this step.

It is when I look in my answer key and see that cosA = - 24/25 and sinB = -40/41 that I am confused: why are they negative?

Here's what I already know:

• Cosine is postive in quadrants 1 & 4
• Sin is postive in quadrants 1 & 2
• Tan is postive in quadrants 1 & 3
• Neither point A or point B are in quadrant 1

Still, I don't understand why its negative, I'm having a brain block here.

HI

sin A is positive . Since it cant be in the first quadrant , then it must be in the second quadrant . That follows why cos A is negative .

cos B is positive , and it cant be in the first quadrant so it must be in the fourth quadrant , and sin B is negative here .

then use the sin formulas to expand and substitute appropriately .
• Nov 15th 2009, 07:48 AM
saintv
Thank you!