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Math Help - Finding where a function = 0

  1. #1
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    Finding where a function = 0

    I have the following:

    20cos(5t) + 4sin(5t) = 0

    So I can get to

    tan(5t) = -5

    then take arctan(-5) to get -1.3...(something) but I'm unsure how to proceed? I need the amplitude/wavelength of this function, more specifically I need to find where the first and second time it = 0 after the first initial t=0

    Usually I end up with a pi answer, for example another I solved ended up as

    tan(4t) = -1

    and I solved for 3pi/16 and 7pi/16.

    I'm stuck with this one however, any help would be great.
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  2. #2
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    Re: Finding where a function = 0

    Quote Originally Posted by fourierT View Post
    I have the following:
    20cos(5t) + 4sin(5t) = 0
    So I can get to
    tan(5t) = -5

    then take arctan(-5) to get -1.3...(something) but I'm unsure how to proceed? I need the amplitude/wavelength of this function, more specifically I need to find where the first and second time it = 0 after the first initial t=0.
    Have you looked at this calculation?
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  3. #3
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    Re: Finding where a function = 0

    Quote Originally Posted by Plato View Post
    I did but I didn't really understand how to find the first two times when the function = 0 after the initial t=0, I know that the solutions contain an n because there are infinitely many solutions, but how do I find the first 3 only?
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  4. #4
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    Re: Finding where a function = 0

    Let $n=0$, $n=1$, $n=2$, etc. Each time you increase $n$, you get a larger $t$ value. Put them in order, and take the first three.
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  5. #5
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    Re: Finding where a function = 0

    Quote Originally Posted by SlipEternal View Post
    Let $n=0$, $n=1$, $n=2$, etc. Each time you increase $n$, you get a larger $t$ value. Put them in order, and take the first three.
    How do I know how far to go though?
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  6. #6
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    Re: Finding where a function = 0

    You said you wanted 3? I would say go up to $n=3$.
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  7. #7
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    Re: Finding where a function = 0

    Quote Originally Posted by SlipEternal View Post
    You said you wanted 3? I would say go up to $n=3$.
    I'm getting answers that are very hard to interpret in terms of wavelength?
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  8. #8
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    Re: Finding where a function = 0

    Quote Originally Posted by fourierT View Post
    I'm getting answers that are very hard to interpret in terms of wavelength?
    Why? Wavelength is easy to calculate. It is $\dfrac{2\pi}{5}$.
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