How do you convert # (-1,1)# into polar form?
1 Answer
Sep 22, 2016
Explanation:
To convert from
#color(blue)"cartesian to polar form"# That is
#(x,y)to(r,theta)#
#color(orange)"Reminder " color(red)(bar(ul(|color(white)(a/a)color(black)(r=sqrt(x^2+y^2))color(white)(a/a)|)))# and
#color(red)(bar(ul(|color(white)(a/a)color(black)(theta=tan^-1(y/x))color(white)(a/a)|)))# here x = -1 and y = 1
#rArrr=sqrt((-1)^2+1^2)=sqrt2# Now (-1 ,1) is in the 2nd quadrant so we must ensure that
#theta# is in the 2nd quadrant.
#theta=tan^-1(-1)=-pi/4larr" related acute angle"#
#rArrtheta=(pi-pi/4)=(3pi)/4# Thus
#(-1,1)to(sqrt2,(3pi)/4)#