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Math Help - Does this Look right?

  1. #1
    Member M670's Avatar
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    Does this Look right?

    Suppose
    and is negative. Here are some small variations on the previous problems:






    Which one of the two addition formals would put me on the right way?
    sin(u-pi)=sin(u)cos(pi)-cos(u)sin(pi)
    or
    sin(-(12/13)-pi)= sin-(12/13)cos(pi)-cos-(12/13)sin(pi)?
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Does this Look right?

    I would use:

    \sin(u)=-\sqrt{1-\cos^2(u)}

    \sin(u-\pi)=-\sin(\pi-u)=-\sin(u)

    \cos(u-\pi)=\cos(\pi-u)=-\cos(u)

    \sin\left(u-\frac{\pi}{2} \right)=-\sin\left(\frac{\pi}{2}-u \right)=-\cos(u)

    \cos\left(u-\frac{\pi}{2} \right)=\cos\left(\frac{\pi}{2}-u \right)=\sin(u)
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  3. #3
    Member M670's Avatar
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    Re: Does this Look right?

    Quote Originally Posted by MarkFL2 View Post
    I would use:

    \sin(u)=-\sqrt{1-\cos^2(u)}

    \sin(u-\pi)=-\sin(\pi-u)=-\sin(u)

    \cos(u-\pi)=\cos(\pi-u)=-\cos(u)

    \sin\left(u-\frac{\pi}{2} \right)=-\sin\left(\frac{\pi}{2}-u \right)=-\cos(u)

    \cos\left(u-\frac{\pi}{2} \right)=\cos\left(\frac{\pi}{2}-u \right)=\sin(u)
    Thank You very much, So the initial cos (u)=5/13 has nothing to do with the other problems? I thought I had to relate each one to the original somehow
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  4. #4
    Member M670's Avatar
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    Re: Does this Look right?

    But the other problem is when I input your answers the program tells me variable "u" is not defined in this context?
    meaning these answers it will consider wrong
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  5. #5
    MHF Contributor MarkFL's Avatar
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    Re: Does this Look right?

    You are given the value of cos(u), then from this you may find sin(u) using the first formula, and since you now have sin(u) and cos(u), the rest come from that.
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  6. #6
    Member M670's Avatar
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    Re: Does this Look right?

    but sin(u) is -(12/13)
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  7. #7
    Member M670's Avatar
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    Re: Does this Look right?

    Which would mean sin(u-pi) should be Sin(u-pi)= sin-(12/13)cos(pi)-cos-(12/13)(sin(pi)
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  8. #8
    MHF Contributor MarkFL's Avatar
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    Re: Does this Look right?

    If sin(u) = -12/13, then -sin(u) = 12/13.
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