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Thread: Help with Cosine Function

  1. #1
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    Exclamation Help with Cosine Function

    What function is y = cos(x + π) equal to

    can you also explain the answer

    thanks
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Help with Cosine Function

    Use the angle-sum identity for cosine:

    $\displaystyle \cos(\alpha+\beta)=\cos(\alpha)\cos(\beta)-\sin(\alpha)\sin(\beta)$

    You may also think of the unit circle. Pick an arbitrary point on the circle. The counter-clockwise angle to the radius at this point as measured from the positive x-axis is the angle $\displaystyle \theta$. The x-coordinate of this point is $\displaystyle \cos(\theta)$. To add $\displaystyle \pi$ radians to this angle, go to the point on the opposite side of the circle, on the other end of the diameter. Can you see what relation the new x-coordinate will always have with the original?
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  3. #3
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    Re: Help with Cosine Function

    $\displaystyle \sin(x + \frac{\pi}{2}) = \cos(x)$

    $\displaystyle \cos(x + \frac{\pi}{2}) = -\sin(x)$

    $\displaystyle -\sin(x + \frac{\pi}{2}) = -\cos(x)$

    $\displaystyle -\cos(x + \frac{\pi}{2}) = \sin(x)$

    Whenever you add $\displaystyle \frac{\pi}{2}$ to the input you shift it to the left by Pi/2, so when you add Pi, you do that twice, so you effectively move from cos to -cos. So

    $\displaystyle \sin(x + \pi) = -\sin(x)$
    $\displaystyle \cos(x + \pi) = -\cos(x)$
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