The graph of a limacon curve is given. without using your graphing calculator, determine which equation is correct for the graph.
r = 2 + 2 sin θ
r = 3 + 2 sin θ
r = 1 + 3 sin θ
r = 3 + sin θ

  r = 3 + sin(θ)

Step-by-step explanation:

The curve extends below the x-axis, so the added constant must be larger than the coefficient of the sine function. There are two choices matching that description.

The extent in the -y (θ=-π/2) direction looks to be about 2/3 of the extent in the +x (θ=0) direction, so we expect the appropriate equation is ...

  r = 3 + sin(θ)