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Math Help - Need help with finding exact value

  1. #1
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    Need help with finding exact value

    Given that q = sin  1( 3/5)find the exact value of sin (1/3π+ q)." alt="sin (1/3π+ q)." />
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  2. #2
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    Hello, perryman!

    Given that: . q \,=\, \sin^{ 1}\left(-\,\frac{3}{5}\right)

    find the exact value of: . \sin\left(q + \frac{\pi}{3}\right)

    We have: . q \;=\;\sin^{-1}\left(-\,\frac{3}{5}\right)

    Then: . \sin q \;=\;-\frac{3}{5} \;=\;\frac{opp}{hyp}

    q is an angle in a right triangle with: opp = -3,\;hyp = 5
    . . Pythagorus says: . adj = \pm4
    Hence: . \cos q \,=\,\pm\frac{4}{5}


    We have: . \sin\left(q + \frac{\pi}{3}\right) \;=\;\sin q\cos\frac{\pi}{3} + \cos q\sin\frac{\pi}{3}

    . . . . . . . . . . . . . =\;\left(-\frac{3}{5}\right)\left(\frac{1}{2}\right) + \left(\pm\frac{4}{5}\right)\left(\frac{\sqrt{3}}{2  }\right)

    . . . . . . . . . . . . . =\;-\frac{3}{10} \pm\frac{4\sqrt{3}}{10}

    . . . . . . . . . . . . . =\; \frac{-3 \pm 4\sqrt{3}}{10}

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