How do you find the polar coordinates given the rectangular coordinates #(-2,-5)#?

1 Answer
Jim G.
Nov 5, 2016

#(sqrt29,4.33)#

Explanation:

To convert from #color(blue)"rectangular to polar coordinates"#

That is #(x,y)to(r,theta)#

#color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(r=sqrt(x^2+y^2))color(white)(2/2)|)))#

and #color(red)(bar(ul(|color(white)(2/2)color(black)(theta=tan^-1(y/x))color(white)(2/2)|)))#

here x = - 2 and y = - 5

#rArrr=sqrt((-2)^2+(-5)^2)=sqrt(4+25)=sqrt29#

Now (-2 ,-5) is in the third quadrant so we must ensure that #theta# is in the third quadrant.

#theta=tan^-1(5/2)=1.19" radians"larr" reference angle"#

#rArrtheta=(pi+1.19)=4.33#

#rArr(-2,-5)to(sqrt29,4.33)to(sqrt29,248.2^@)#

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