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Thread: Trigonometric Phase Lines

  1. #1
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    Trigonometric Phase Lines

    Hi,
    As part of a recent assignment I have been asked to draw a phase line for the function $\displaystyle \frac{dy}{dt} = sin(y)$. I can find the main equilibrium point easily ($\displaystyle y = 0$) but the problem I have is that $\displaystyle y = 180, y = 360, y = 540$ are also solutions. So in a way I have a phase line that continues infinitely. Is there any formal way of setting this out. The main idea that comes to mind is including an algebraic multiplier of both 180 and -180 on the phase line the stating $\displaystyle a \in Z$ when $\displaystyle a$ is the multiplier.

    Thoughts?
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  2. #2
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    Usually with trig functions, one will write $\displaystyle k\pi$. That way for any integer you will hit all multiples of $\displaystyle \pi$ or $\displaystyle 180$
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  3. #3
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    thanks dwsmith I figured it would be something like that.
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