Question

What is the Cartesian form of `(5,(3pi )/2)`?

Answer 1

The cartesian point is `(0,-5)`.

Explanation:

`x=rcos(theta)` and `y=rsin(theta)` and for the given point `r=5` and `theta=(3pi)/2`.

`x=5cos((3pi)/2)=5*0=0`
`y=5sin((3pi)/2)=5*(-1)=-5`

So the cartesian point is `(0,-5)`.

Answer 2

`(0,-5)`

Explanation:

`"to convert from "color(blue)"polar to cartesian form"`

`"that is "(r,theta)to(x,y)" where"`

`•color(white)(x)x=rcostheta" and "y=rsintheta`

`"here "r=5" and "theta=(3pi)/2`

`rArrx=5xxcos((3pi)/2)=5xx0=0`

`rArry=5xxsin((3pi)/2)=5xx-1=-5`

`rArr(5,(3pi)/2)to(0,-5)`