Chapter 9.1, Problem 33E

To determine

To draw: the polar equation.

Explanation of Solution

Given information:

The polar equation is $\theta =\frac{5\pi }{4}$ .

Graph: to draw the equation, the solution to this equation are the ordered pairs $\left(r,\theta \right)$ where $\theta =\frac{5\pi }{4}$ and $r$ is any real number.

Some points are $\left(1,\frac{5\pi }{4}\right),\left(-2,\frac{5\pi }{4}\right),\left(3,\frac{5\pi }{4}\right)$ .

The graph of the polar equation is the set of all ordered pairs of the form $\left(r,\frac{5\pi }{4}\right)$ .

The graph is the line that includes the terminal side of the angle $\frac{5\pi }{4}$ in standard position.

The graph can be obtained as:

  

Interpretation: from the above graph it can be observed that the type of curve of polar equation is line.