Question

What are the polar coordinates of `(0, −4)`?

Answer 1

`4/_pi`

Explanation:

To convert rectangular co-ordinates `(x,y)` into polar co-ordinates `(r/_theta)`, we may use the conversion factors which may be derived from a simple right-angled triangle and basic trigonometry :

`x=rcostheta and y=rsintheta`
`x^2+y^2=r^2 and theta=tan^(-1)(y/x)`

So in this case, `r=sqrt(0^2+4^2)=4`
Since the point `(0,-4)` lies on the negative x-axis, `=>theta=pi`.

So the polar representation of the point (or vector) is `4/_pi`.