Question

What is the Cartesian equivalent of polar coordinates `(7, pi)`?

Answer 1

In this problems we know that `(r,theta)->(7,pi)`.

We also know the following equations are used to convert polar coordinates to rectangular coordinates.

`(x,y)->(rcos(theta),rsin(theta))`

Substitute in the values for `r` and `theta`

`(x,y)->(7cos(pi),7sin(pi))`

Remember back to the unit circle

`cos(pi)=-1`
`sin(pi)=0`

Substitute in those values

`(x,y)->(7(-1),7(0))`

Simplify

`(x,y)->(-7,0)`