How do you convert the following to polar coordinates #2xy=1#?

1 Answer
Jan 8, 2016

Answer:

I think the question is convert to a polar equation. You use the rectangular conversion equations.

Explanation:

Based on the circular definitions of the trigonometric functions of sine and cosine you have the following:
#sin theta = y/r# and #cos theta=x/r#.

therefore:

#y=rsintheta# using algebra and
#x=rcostheta# using algebra.
These are the conversion from rectangular #(x,y)# to polar #(r,theta)#

So in the equation #2xy=1# you simply substitute.

#2*rcostheta*rsintheta=1#
#2costheta*sintheta*r^2=1#
#sin(2theta)*r^2=1#

so your polar equation is:

#r^2=csc^2(2theta)#