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Math Help - Sum/Difference Identity

  1. #1
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    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.
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  2. #2
    MHF Contributor
    Joined
    Sep 2008
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    West Malaysia
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    Quote Originally Posted by saintv View Post
    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 .
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  3. #3
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    Thank you!
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