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Math Help - 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:

    \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 \theta. The x-coordinate of this point is \cos(\theta). To add \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

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

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

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

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

    Whenever you add \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

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