What is the Cartesian form of #(-2,(88pi) /16)#?

1 Answer
Alan P.
Sep 8, 2016

Polar #(r,theta)=(-2,(88pi)/16)# is equivalent to Cartesian #(x,y)=(0,2)#

Explanation:

#theta=(88pi)/16=5pi +pi/2#
Since #2pi# makes one full circle
#(88pi)/16# is equivalent to #(3pi)/2#

As an angle #(3pi)/2# maps on to the negative Y-axis in the Cartesian system.

The polar point #(-2,(88pi)/16)# is therefore a distance of #(-2)# from the origin measured down the negative Y-axis;
but #(-2)# down the negative Y-axis is the same as #+2# up the positive Y-axis.

Therefore #(-2,(88pi)/16)# is a point on the Y-axis at #y=2#;
that is at #(x,y)=(0,2)#

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