Question

Given the (x,y) coordinates of a point are (-1,-2) find 2 different (r, feta) coordinates?
one with r > 0 and one with r< 0.

a. Feta between zero and 2pie
b. Feta between negative pie and pie
c. Feta between 2pie and 4pie

Answer 1

Does your instructor really say "feta" ?
If you listen carefully it is probably "theta"

Make a sketch , and plot (-1,-2)
join it to the origin.
Length of line = √(1+4) = √5
the angle is in the 3rd quadrant
tanØ = -2/1 = 2
Ø = 1.107 in I or Ø = 1.107+π = 4.248

so one possibility is (√5, 4.248) using r>0
or (-√5, 1.107) using r < 0

adding or subtracting or subtracting 2π will end up in the same location
so I will let you create points with the given conditions of
a), b), and c)