Consider the polar graphs, r = 1 - sin θ and r = sin θ, shown in the figure below.
a. Find the polar coordinates (r, θ) for all the points of intersection on the figure.
b. Find the area of the region that lies inside both the graph of r = 1 - sin θ and r = sin θ.
c. Find the slope of the line tangent to the graph of r = 1 -sin θ at θ = π.
d. Find the Cartesian equation for the line tangent to the graph of r = 1 - sin θ at θ = π.