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Given an angle $\theta$ (in radians), write $\theta = 2\pi t + \phi$, where $\phi$ is between $0$ and $2\pi$, $0\leq \phi\lt 2\pi$, and $t$ is an integer. Call $k=2\pi t$ the number of "full circles" or "full turns" corresponding to the angle.

If $\theta = \frac{13\pi}{4}$, am I right that k=$2\pi$?

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    @Arturo A little $p$oliteness and patience for someone on their first question please.2010-11-30

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I'm guessing that the homework problem is something like "find an angle between 0 and $2\pi$ that's equal to $13\pi/4$". That is, for what $k$ such that $k$ is a multiple of $2\pi$ do we have $ {13\pi\over 4} = k + {5\pi\over 4}$

The answer is indeed $k=2\pi$. The first equation in the original question should just have "$k$" in place of "($2\pi$)".