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

1 Answer
Trevor Ryan.
Nov 5, 2015

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.

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