Question

How do you find the polar coordinates of the rectangular point (-4,4)?

Answer 1

`sqrt32/_-pi/4`

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(4^2+4^2)=sqrt32`
`theta=tan^(-1)(4/-4)=-pi/4`.

So the polar representation of the point (or vector) is `sqrt32/_-pi/4`.