What is the polar form of #( -1,-2 )#?

2 Answers
Mar 26, 2016

polar coordinate #(sqrt5,tan^-1 2)#

Explanation:

#x= rcos theta and y =rsintheta#
here # x = -1 and y = -2#
the point is in third quadrant
So# tantheta = y/x=(-2)/-1=2#
as the point is in 3rd coordinate
#:. theta = pi+tan^-1 2#
and #r = sqrt(x^2+y^2)=sqrt5#

polar coordinate #(sqrt5,pi+tan^-1 2)#

Mar 26, 2016

#(sqrt5, pi+tan^(-1)2)#

Explanation:

The equations #x = -1 = r cos theta and y = -2 = r sin theta # give
r = #sqrt(x^2+y^2)=sqrt5#.

To find #theta#, observe that both #sin theta# and #cos theta# are negative. The angle is in the third quadrant. The first quadrant angle #theta=tan^(-1)2#. The angle for the opposite direction is the correct value for #theta#.i

#tan (pi+theta) = tan theta#
So, #theta=pi+tan^(-1)2#. .