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Math Help - If blahblah, Find the exact value of

  1. #1
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    If blahblah, Find the exact value of

    if sina=12/13 and pi/2 < a < pi, cosB= -4/5 and pi < B < 3pi/2, find the exact value of,

    a) sin(a+B)
    b)cos(a+B)
    c) tan(a+B)

    Could someone please explain how to do this? ^^
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  2. #2
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    Remember that \displaystyle \sin^2{\theta} + \cos^2{\theta} = 1.

    You can use this fact to find the values of \displaystyle \cos{a} (remembering that it is in the second quadrant) and \displaystyle \sin{B} (remembering that it is in the third quadrant).

    Using these, you can find the tangent values using \displaystyle \tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}.


    Then use the identities

    \displaystyle \sin{(\alpha \pm \beta)} = \sin{\alpha}\cos{\beta} \pm \cos{\alpha}\sin{\beta}

    \displaystyle \cos{(\alpha \pm \beta)} = \cos{\alpha}\cos{\beta} \mp \sin{\alpha}\sin{\beta}

    \displaystyle \tan{(\alpha \pm \beta)} = \frac{\tan{\alpha} \pm \tan{\beta}}{1 \mp \tan{\alpha}\tan{\beta}}.
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  3. #3
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    Thanks a lot.
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