How do you convert #(-3, 3)# into polar coordinates?
1 Answer
Apr 20, 2018
Explanation:
#"to convert from "color(blue)"cartesian to polar"#
#"that is "(x,y)to(r,theta)" where"#
#•color(white)(x)r=sqrt(x^2+y^2)#
#•color(white)(x)theta=tan^-1(y/x);-pi< theta<= pi#
#"here "x=-3" and y=3#
#rArrr=sqrt((-3)^2+3^2)=sqrt18=3sqrt2#
#(-3,3)" is in the second quadrant so "theta" must be in the "#
#"second quadrant"#
#theta=tan^-1(1)=pi/4larrcolor(red)"related acute angle"#
#rArrtheta=pi-pi/4=(3pi)/4larrcolor(red)"in second quadrant"#
#rArr(-3,3)to(3sqrt2,(3pi)/4)#
