How do you convert #(-5, -5)# into polar form?

1 Answer
Alan P.
Nov 3, 2016

Cartesian: #(x,y)=(-5,-5)#
#color(white)("XXX")#Polar: #(r,theta)=(5sqrt(2),(5pi)/4)#

Explanation:

#(-5,-5)# is a point in Quadrant III (since both #x# and #y# components are negative.

The #x# and #y# components are equal, so the reference angle is #pi/4#.
If the reference angle is #pi/4# and the angle is in Q III,
then the angle is #pi+pi/4=(5pi)/4#

The radius is the length of the hypotenuse; with an angle of #pi/4# the length of the hypotenuse is #sqrt(2) xx abs("length of side")#

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