What are the polar coordinates of #(−2, −9)#?

1 Answer
Jim G.
May 4, 2017

#(sqrt85,-1.79)#

Explanation:

#"to convert from "color(blue)"cartesian to polar coordinates"#

#"that is " (x,y)to(r,theta)" where"#

#• r=sqrt(x^2+y^2)#

#• theta=tan^-1(y/x);-pi < theta <= pi#

#rArrr=sqrt((-2)^2+(-9)^2)=sqrt85#

#(-2,-9)" is in the third quadrant so must ensure that "#
#theta" is in the third quadrant"#

#theta=tan^-1(9/2)=1.35larr" related acute angle"#

#rArrtheta=-pi+1.35=-1.79larr" in third quadrant"#

#rArr(-2,-9)to(sqrt85,-1.79)#

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