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Math Help - Trigonometric equation trouble

  1. #1
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    Trigonometric equation trouble

    So there was an equation that I didn't quite understand, and I was hoping somebody could give me some insight. Here it goes...

    Find ALL solutions to the equation: 3sintcost = 3cost

    it was on mymathlab and the solution box was set up something like this: t = ____, where N is any integer.



    the correct answer was: pi/2 + pi*N


    my answer was: pi/2 + 2pi*N



    *** I do not understand why it is "+ pi*N", because the sine and cosine functions have a periodicity of 2pi.

    can someone explain why it is simply "+ pi*N" instead of "+ 2pi*N"??
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Trigonometric equation trouble

    I factored the equation as follows:

    3\cos(t)(\sin(t)-1)=0

    Now, where \sin(t)=1 we also have \cos(t)=0, so we need only concern ourselves with this, and for:

    \cos(t)=0

    we find:

    t=\frac{\pi}{2}+N\pi=\frac{\pi}{2}(2N+1)

    In other words, we want odd integer multiples of \frac{\pi}{2}.
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  3. #3
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    Re: Trigonometric equation trouble

    I would like to add that the equation gets reduced to 3cos(t) ( sin(t) - 1)= 0
    That implies either sin (t) = 1 or cos (t) = 0
    We know that sin(t) = 1 when the terminal arm of angle t is at y axis. That has been rightly been explained that is t will be an odd multiple of pi/2
    cos(t) = 0 when the terminal arm of angle t is at x axis that is when t is and even multiple of pi/2
    now combining the two solutions we conclude that t = odd or even multiple of pi/2
    and that means n * pi/2 when is any integer.
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: Trigonometric equation trouble

    \cos(t)=0 at odd multiples of \frac{\pi}{2}...at even multiples we have |\cos(t)|=1.
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  5. #5
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    Re: Trigonometric equation trouble

    Quote Originally Posted by MarkFL View Post
    \cos(t)=0 at odd multiples of \frac{\pi}{2}...at even multiples we have |\cos(t)|=1.
    You are right i stand corrected. In both the cases t has to be odd multiple of pi/2
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