Question

what are the horizontal and vertical intercepts :r=4-4cos(theta) please show work

Answer 1

x=-9 x=0
y-4
y=0
y=-4

Answer 2

You will run horizonally if θ is zero or θ = 180°
so r = 4 - 4cos0 = 0 , which corresponds to (0,0) in cartesian coordinates
or r = 4 - 4cos180 = 8 , which corresponds to (-8,0)

to run vertically θ = 90 or θ = 270
if θ=90° , r = 4 - 4cos90 = 4 , which corresponds to (0,4)
if θ = 270, r = 4 - 0 = 4, which corresponds to (0,-4)

check: https://www.wolframalpha.com/input/?i=polar+plot+r%3D4-4cos%CE%B8