Question

graph each pair of polar equations on the same polar grid. Find the polar coordinates of the point(s) of the intersection and label the point(s) on the graph.

$$\begin{gathered} r=8\sin \theta \\ r=4csc\theta \end{gathered}$$

Short answer

The polar coordinates of the points of intersection of $r=8\sin \theta \&r=4csc\theta$are $\left(5.65,\frac{\mathrm{\pi }}{4}\right)\&\left(5.65,\frac{3\mathrm{\pi }}{4}\right)$and the graph is

Step-by-step solution

Step 1. Given Information  

The given equations are
$$\begin{gathered} r=8\sin \theta \\ r=4csc\theta \end{gathered}$$

Step 2. Graph of equation  

Plot the graph of equations $r=8\sin \theta \&r=4csc\theta$on the same polar grid

The graph state that the coordinates of the points of intersection are$\left(5.65,\frac{\mathrm{\pi }}{4}\right)\&\left(5.65,\frac{3\mathrm{\pi }}{4}\right)$