Chapter 10.6, Problem 1AYU

To determine

To fill: The $x$ and $y$ in terms of $r$ and $\theta$, if $\left(x,y\right)$ are the rectangular coordinates of a point $P$ and $\left(r,\theta \right)$ are its polar coordinates then x =____ and y =____.

Answer to Problem 1AYU

$x=r\text{cos}\theta$, $y=r\text{sin}\theta$

Explanation of Solution

Given:

$\left(x,y\right)$ are the rectangular coordinates of a point $P$ and $\left(r,\theta \right)$ are its polar coordinates.

Calculation:

If $P$ is a point with polar coordinates $\left(r,\theta \right)$, the rectangular coordinates $\left(x,y\right)$,

Then,

$x=r\text{cos}\theta$

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

where $r²=x²+y²$.