Give the smallest value for 'a' to complete the graph

Question

The curve $r=5\sinθ$ is given for $0\leθ\le a$
It appears that if $a = \pi$, the graph is complete. Now my question is why? Since I thought it should be $a = 2\pi$ since $2\pi = 360°$, which is a full circle.

Answer 1

If you plot the points at some spacing of $\theta$ you will see the graph is complete when $\theta=\pi$. Because of the relationship $\sin (\theta+\pi)=-\sin (\theta)$ as $\theta$ rises from $\pi$ to $2\pi$ you have $r$ being negative, which reflects the angle through the center and retraces the graph you have already plotted.