Question

What are the components of the vector between the origin and the polar coordinate `(4, (3pi)/2)`?

Answer 1

Horizontal component `x=0`
Vertical component `y=-4`

Explanation:

For a vector `(r,theta)` in polar form, the rectangular components are given by

`x=rcostheta and y=rsintheta`.

So in this case, the horizontal component is given by `x=4cos((3pi)/2)=0`.

The vertical component is then `y=4sin((3pi)/2)=-4`.