Question

How do you find the corresponding rectangular coordinates for the point `( 4, (3pi)/2 )`?

Answer 1

`(0,-4)`

Explanation:

`(4,(3pi)/2)=(r,theta)`

for Polars

`x=rcostheta`

`:.x=4cos((3pi)/2)`

`x=4xx0=0`

`y=rsintheta`

`y=4xxsin((3pi)/2)`

`y=4xx-1=-4`

`(0,-4)`

Answer 2

The coordinates are `(0,-4)`. See explanation.

Explanation:

To transform a point in polar coordinates `(r,varphi)` to Carthesian coordinates `(x,y)` you use the formulas:

`{(x=rcosvarphi),(y=rsinvarphi):}`

In the given example we get:

`{(x=4cos((3pi)/2)),(y=4sin((3pi)/2)):}`

`{(x=4*0),(y=4*(-1)):}`

So the answer is:

`{(x=0),(y=-4):}`