Chapter 9.1, Problem 76AYU

In Problems 69-76, the letters $r\text{ and }\theta$ represent polar coordinates. Write each equation using rectangular coordinates $\left(x,y\right)$.

$r\text{ = }\sin \theta \text{ + 1}$

To determine

To find: Equation using rectangular coordinates $(x,y)$. The Letters $r\text{and}\theta$ represent polar coordinates.

Answer to Problem 76AYU

Solution:

$x^2+y^2-y-\sqrt{x^2+y^2}=0$

Explanation of Solution

Given:

$r=\sin \theta +1$

Calculation:

Use the formula,

$x=r\cos \theta$   $y=r\sin \theta$

We have,

$r=\sin \theta +1$

Multiplying $r$ on both sides we have,

$r^2=r\sin \theta +r$

Using the formula $r^2=x^2+y^2$ we have,

$x^2+y^2=y+\sqrt{x^2+y^2}$

$x^2+y^2-y-\sqrt{x^2+y^2}=0$