Question

Special Polar Equations

Match the polar equation with the graphs labeled$I-IV$ . Give reasons for your answers$r=\sin \left(\frac{\theta }{2}\right)$

Short answer

Graph of the given equation is matched with iv

Step-by-step solution

Step 1. Given information

A polar equation is given as $r=1+c\sin 2\theta$

Step 2. Concept used

Choose the domain of the angle first. Find r for different$\theta$ . Plot the graph then match with the given four.

Step 3. Calculation

The domain is $0\le \theta \le 4\pi$