Chapter 14.3, Problem 25WE

To determine

To find: The equivalent rectangular-coordinate equation for the given polar equation.

Answer to Problem 25WE

  $y=2$

Explanation of Solution

Given information:

An equation in polar coordinate is given as $r\sin \theta =2$ .

Concepts used: Conversion formula for coordinate systems are given as-

1. From polar to rectangular:

  $x=r\cos \theta$

  $y=r\sin \theta$

2. From rectangular to polar:

  $r^2=x^2+y^2\Rightarrow r=\pm \sqrt{x^2+y^2}$

  $\cos \theta =\frac{x}{r}$ ; $\sin \theta =\frac{y}{r}$ ; $\tan \theta =\frac{x}{y}$ .

Calculation:

Given equation in polar-coordinate is $r\sin \theta =2$ .

Converting into equivalent rectangular-coordinate equation -

  $\begin{array}{l}r\sin \theta =2\\ \text{Put }x=r\cos \theta ,y=r\sin \theta ,\\ \Rightarrow y=2\end{array}$

Hence, desired equivalent rectangular-coordinate equation would be $y=2$ .