Question

What are the components of the vector between the origin and the polar coordinate `(12, (pi)/2)`?

Answer 1

Horizontal component is `0` and vertical component is `12`.

Explanation:

This point lies on the positive y-axis 12 units from the origin, since the polar angle is defined as an anti-clockwise turn from the positive x-axis. Hence its rectangular form is `0hati + 12hatj`.
Proof:
Convert this vector to rectangular form using the transformations from `(r,theta) to (x,y)` as follows

`x=rcostheta and y=rsintheta`

`thereforex=12cos(pi/2)=0`

`y=12sin(pi/2)=12`

This verifies its components as mentioned above.