period of polar curves curves

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Given a polar curve in the form $r=a+b\cos(k \theta)$,how can I find the length of the interval for which the curve has its complete form? (I'm looking for the period of such curves)

I'm asking this question,since I think it's necessary for plotting the graph of such polar curves.

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$ k \theta\;$ varies between $0- 2 \pi$

If $k=3,\;$ then the period is $\dfrac {2 \pi}{3}$

If $k=\dfrac12,\; $ then the period is ${4 \pi}.$

Polar plot for $ k= 3$ has period $\theta =!20^{\circ}$. This is the period; in other words angular difference between consecutive maximum radii or minimum radii.

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