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I´m currently using polar coordinates to calculate some double and triple integrals. However, I have an small doubt; when you are want to express, lets say, a circle of radius $a$ centered in $(a,0)$ you can write it in polar coordinates and say that $x=r\cos\theta $ .and $y=r\sin \theta $ and so, as $(x-a)^2+y^2=a^2$, then $r=2a\cos\theta$.

My question is: Why is it that $-\pi/2<\theta<\pi/2$?

Please excuse me for such a dull question.

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The graph of $r = 2a \cos \theta$ for $-\pi < \theta \leq \pi$ is a sideways figure 8, with the circle you want on the right, and the circle you don't want on the left. The circle on the left is obtained from $-\pi < \theta \ -\pi/2$ (lower half) and $\pi/2 \leq \theta \leq \pi$ (upper half). So to get just your one circle you have to restrict the range to not use those values.

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