Please help with a, b, and c

Question

Plot the point [−4,−π/4]​, given in polar​ coordinates, and find other polar coordinates

(r,θ) of the point for which the following are true.

​(a) r>0, −2π≤θ<0          

​(b) r<0, 0≤θ<2π          

​(c) r>0,

Answer 1

Since polar coordinates are (r, θ), then r = -4 and θ = -π/4. A negative radius (r) is the opposite side (180° off) of the positive radius so in this diagram I've shown the positive 4 radius in red as a reference:

Once you get to the red dot (going out to r = 4 and going CW to -π/4) you go to the opposite side of the circle to get to (-4, -π/4).

For r > 0 with θ on (0, 2π], the "blue dot" point is (4, 3π/4)

For r < 0 with θ on (0, 2π], the "blue dot" point is (-4, 7π/4)