How do you convert #(-1,-3)# from cartesian to polar coordinates?

1 Answer
Feb 4, 2018

#(sqrt10,-1.893)#

Explanation:

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

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

#•color(white)(x)r=sqrt(x^2+y^2)#

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

#"here "x=-1" and "y=-3#

#rArrr=sqrt((-1)^2+(-3)^2)=sqrt10#

#theta=tan^-1(3)=1.249larrcolor(blue)"related acute angle"#

#(-1,-3)" is in the third quadrant so "theta" must be in the"#
#"the third quadrant"#

#rArrtheta=(-pi+1.249)=-1.893#

#rArr(-1,-3)to(sqrt10,-1.893)#