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Math Help - Compound Angle

  1. #1
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    Compound Angle

    Angle a lies in the second quadrant and angle b lies in the third quadrant such ath cos a = -3/5 and tan b = 24/7

    determine an exact value for
    cos(a+b)
    and
    sin (a-b)

    I got cos(a+b) = cosacosb - sinasinb
    =(-3/5)(-7/25) - (4/5)(-24/25)
    = 117/125

    i am not sure if this is right, but i am also completely lost for sin (a-b)
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  2. #2
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    Quote Originally Posted by Johnny123321 View Post
    Angle a lies in the second quadrant and angle b lies in the third quadrant such ath cos a = -3/5 and tan b = 24/7

    determine an exact value for
    cos(a+b)
    and
    sin (a-b)

    I got cos(a+b) = cosacosb - sinasinb
    =(-3/5)(-7/25) - (4/5)(-24/25)
    = 117/125

    i am not sure if this is right, but i am also completely lost for sin (a-b)
    It will help if you recall the 3-4-5 Right-angle triangle, and the 7-24-25 Right-angle triangle.
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    check

    can you help me check if i did cos (a+b) right
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    Quote Originally Posted by Johnny123321 View Post
    Angle a lies in the second quadrant and angle b lies in the third quadrant such ath cos a = -3/5 and tan b = 24/7

    determine an exact value for
    cos(a+b)
    and
    sin (a-b)

    I got cos(a+b) = cosacosb - sinasinb
    =(-3/5)(-7/25) - (4/5)(-24/25)
    = 117/125

    i am not sure if this is right, but i am also completely lost for sin (a-b)
    If a is in quadrant 2, then \sin{a} > 0, \cos{a} < 0 and \tan{a} < 0.

    If b is in quadrant 3, then \sin{b} < 0, \cos{b} < 0 and \tan{b} > 0.

    If you remember this as well as the 3-4-5 Right-angle triangle and the 7-24-25 Right-angle triangle, you will be fine.
    Last edited by mr fantastic; November 10th 2009 at 04:20 AM. Reason: Moved from double posted question thread
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  5. #5
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    The first part looks correct to me.

    sin(A-B)=sinAcosB-sinBcosA
    (4/5)(-7/25)-(-24/25)(-3/5)
    (-21/25)-(72/125)
    (-93/125)
    Last edited by mr fantastic; November 10th 2009 at 04:21 AM. Reason: No edit - flagging reply as having been moved from duplicate posted question thread.
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