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Math Help - simplify trigonometric

  1. #1
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    simplify trigonometric

    Simplify sin(π/3 - α)
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  2. #2
    Super Member Aryth's Avatar
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    So, we have:

    sin\left(\frac{\pi}{3} - \alpha\right)

    It equals:

    = sin\left(\frac{\pi}{3}\right)cos(\alpha) - cos\left(\frac{\pi}{3}\right)sin(\alpha)

    We know that:

    sin\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}

    And:

    cos\left(\frac{\pi}{3}\right) = \frac{1}{2}

    Therefore:

    = \frac{\sqrt{3}}{2}cos(\alpha) - \frac{1}{2}sin(\alpha)

    = \frac{\sqrt{3} \ cos(\alpha) - sin(\alpha)}{2}

    If it can get any simpler than that... Then I'm lost...
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