How do you find the rectangular coordinates given the polar coordinates #(-2,(4pi)/3)#?

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Answer 1 · 2016-11-21T10:49:08

The rectangular coordinates are #=(1,-sqrt3)#

To convert from polar coordinates #(r,theta)# to recangular coordinates #(x,y)#

We use the following

#x=rcostheta#

and #y=rsintheta#

Here, #(r,theta)= (-2,(4pi)/3)#

#:. x=-2cos((4pi)/3)#

and #y=-2sin((4pi)/3)#

#cos((4pi)/3)=-1/2# and #sin((4pi)/3)=sqrt3/2#

Therefore, #(x,y)=(1,-sqrt3)#