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")#

enter image source here

Related questions
See all questions in Converting Equations from Polar to Rectangular
Impact of this question
4355 views around the world
You can reuse this answer
Creative Commons License