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

1 Answer
Trevor Ryan.
Nov 5, 2015

#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#.

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