Chapter 9.4, Problem 24E

To determine

To graph of the path of the plane .

Explanation of Solution

Given information: The equation is $5=r\cos \left(\theta -\frac{5\pi }{6}\right)$

Graph: Sketch the graph using graphing utility.

  

Interpretation:

  $6=r\cos \theta$ is $6=x$ , which is a vertical line.

  $6=r\cos \left(\theta -{45}^0\right)$ can be obtained by rotating the graph by ${45}^0$ in counterclockwise direction.

If you find this confusing, A simpler way is to write it as follows:

  $\begin{array}{l}6=r\cos \theta \cos \frac{\pi }{4}+r\sin \theta \sin \frac{\pi }{4}\\ 6=\frac{x}{\sqrt{2}}+\frac{y}{\sqrt{2}}\\ 1=\frac{x}{6\sqrt{2}}+\frac{y}{6\sqrt{2}}\end{array}$

Both $x$ and $y$ intercepts are $6\sqrt{2}\approx 8.485$ .