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Math Help - sum/difference identities

  1. #1
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    Angry sum/difference identities

    Hi guys, I thought I knew how to do these but I've done this question over and over on an online test that you can self check answers and I can't get the right answer.

    Here's the situation:

    sin(x)=3/4 1st quadrant
    sin(y)=1/2 2nd quadrant

    As, cos(x)=sqrt(1-sin^2(x))

    cos(x) =sqrt(7)/(4)
    cos(y)=sqrt(-3)/(2)

    cos(x+y)=cos(x)cos(y)+sin(x)sin(y)

    and I get OVER AND OVER this answer: 3/8-sqrt(21)/8

    I spent about half an hour trying to use LaTex to no avail. Sorry.
    If someone can grind out something different and post that'd be wonderful.
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  2. #2
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    Re: sum/difference identities

    Hey guys, I just got it.
    My formula is cos(x+or-y)=cos(x)cos(y)+or-sin(x)sin(y)
    So I assumed that if you were adding angles you'd use addition on the left hand side also, I tried using minus and it worked.. Is that right or is the test wrong?
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  3. #3
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    Re: sum/difference identities

    Quote Originally Posted by camjerlams View Post
    left hand side also
    *right hand side also
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  4. #4
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    Re: sum/difference identities

    The formula is not correct: cos(A+B) = cosAcosB-sinAsinB
    Sin x = 3/4 in first quadrant so cos x will also be positive
    sin y = 1/2 in second quadrant hence cos y will be negative.
    Just plug in the values to get the result.
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  5. #5
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    Re: sum/difference identities

    Note \displaystyle \cos{(y)} = -\frac{\sqrt{3}}{2}, NOT \displaystyle \frac{\sqrt{-3}}{2} as the OP wrote.
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