Question

Find the rectangular coordinates of the point ( -3, 1/2 π)

Answer 1

`x = -3 cos ((\pi)/(2))= 0`

`y = -3 sin ((\pi)/(2))= -3`

And then the rectangular coordinates for this case are :

`(x = 0 , y = -3)`

Explanation:

We have the following point given
`P = (-3, (\pi)/(2))` and we want to conver from polar to rectangular coordinates and we need to use the following formulas:

`x = r cos \theta`

`y = r sin \theta`

For this case we have that:

`r = -3`

And:

`\theta = (\pi)/(2)`

Replacing we got:

`x = -3 cos ((\pi)/(2))= 0`

`y = -3 sin ((\pi)/(2))= -3`

And then the rectangular coordinates for this case are :

`(x = 0 , y = -3)`