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Math Help - in need of a quick response...cos-->sin equation

  1. #1
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    in need of a quick response...cos-->sin equation

    y=-cos2(x-pi/12)
    = -sin2(x-pi/12+3pi/12)
    = -sin2(x+pi/6)

    I don't understand how you get the 3pi/12. If there is another simpler way to get the same answer, please include it.=]
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  2. #2
    o_O
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    This uses the identity: \cos \theta = \sin \left(\theta + {\color{blue}\: \frac{\pi}{2}}\right)

    So looking at your expression: -\cos \left[2 \left(x - \frac{\pi}{12}\right)\right]

    = - \sin \left[2 \left(x - \frac{\pi}{12}\right){\color{blue} \: + \: \frac{\pi}{2}} \: \right]

    = - \sin \left[2 \left(x - \frac{\pi}{12}\right){\color{blue} \: + \: 2\left( \frac{\pi}{4}\right)} \: \right]

    = - \sin \left[2 \left(x - \frac{\pi}{12}{\color{blue} \: + \:  \frac{\pi}{4}}\right) \: \right] (Factored out a 2 of the inside expression)

    etc. etc.
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