Question

How do you convert `(5, (3(pi))/2 )` to rectangular form?

Answer 1

`(0,-5)`

Explanation:

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

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

`•color(white)(x)x=rcosthetacolor(white)(x);y=rsintheta"`

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

`rArrx=5cos((3pi)/2)=0`

`rArry=5sin((3pi)/2)=-5`

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

Answer 2

One should recognize the special case where the angle is `(3pi)/2`

This makes the x coordinate become 0 and makes y coordinate become length of the radial component, 5, overlaid upon the the negative y axis, -5.

Therefore, the point is `(0,-5)`