Chapter 9, Problem 9RE

(a)

To determine

To find:The equationin rectangular coordinates for given polar coordinate.

Answer to Problem 9RE

The equation in rectangular coordinates is $y=x$ .

Explanation of Solution

Given information:

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

Calculation:

The relation between polar coordinates $\left(r,\theta \right)$ , and rectangular coordinates is.

  $\begin{array}{c}{r}^2=x^2+y^2\\ \tan \theta =\frac{y}{x}\end{array}$

Substitute $\tan \theta =\frac{y}{x}$ in $r^2=x^2+y^2$ .

  $y=x$

Therefore, the equation in rectangular coordinates is $y=x$ .

(b)

To determine

To graph:For the equation.

Explanation of Solution

Given information:

The equation is $y=x$ .

Graph:

The graph for the equation is shown in figure (1).

  

Figure (1)

Interpretation:Graph for the equation $y=x$ is shown in figure (1).