Chapter 9.2, Problem 36AYU

In problems 31-38, match each of the graphs $\left(A\right)$ through $\left(H\right)$ to one of the following polar equations.

$r\sin \theta =2$

To determine

To find: Transform the polar equation $r \text{sin}\theta = 2$ to rectangular coordinates equation. Then identify and match the graph.

Answer to Problem 36AYU

Solution

The graph of $r \text{sin}\theta = 2$ is a horizontal line with 2 units above the pole.

From the given graph, option C satisfies the condition of equation of a horizontal line with 2 units above the pole.

Given:

It is asked to the polar equation $r \text{sin}\theta = 2$ to rectangular coordinates and match the graph.

Explanation of Solution

Convert the polar equation to a rectangular equation.

$\begin{array}{}\begin{array}{c}r \text{sin}\theta = 2\\ \left(x, y\right) = \left(r \text{cos}\theta , r \text{sin}\theta \right)\\ y = 2\end{array}\end{array}$

The graph of $r \text{sin}\theta = 2$ is a horizontal line with 2 units above the pole.

To sketch:.

$r \text{sin}\theta = 2$.

From the given graph, option C satisfies the condition of equation of a horizontal line with 2 units above the pole.