Chapter 9.2, Problem 17AYU

In Problems 15-30, transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation.

$r\sin \theta =4$

To determine

To find: Transform the polar equation $r \text{sin}\theta = 4$ to rectangular coordinates. Then identify and graph the equation.

Answer to Problem 17AYU

Solution

The graph of $r \text{sin}\theta = 4$ is a horizontal line with 4 units above the pole.

Given:

It is asked to the polar equation $r \text{sin}\theta = 4$ to rectangular coordinates and graph it.

Explanation of Solution

Convert the polar equation to a rectangular equation.

$r \text{sin}\theta = 4 r^2 = 4$

$\left(x, y\right) = \left(r \text{cos}\theta , r \text{sin}\theta \right)$

$y = 4$

The graph of $r \text{sin}\theta = 4$ is a horizontal line with 4 units above the pole.

To sketch:

$r \text{sin}\theta = 4$