How do you convert # (-1,1)# into polar form?

1 Answer
Jim G.
Sep 22, 2016

#(sqrt2,(3pi)/4)#

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)#

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