Without a calculator, graph the polar function
r = 1 + sin θ
for
0≤ θ ≤ 2π.

Answer

Again, *r* is never negative becauser = 1 + sin θis always between 0 and 2.

Find the value of *r* at some nice angles.

%%%%%%DATA ENTRY This data is in a table.

{c|c}θ& r = 1 + sinθ\hline0&1$\frac{π}{2}$&2π&1$\frac{3π}{2}$&0

This gives us some points to start from.PICTURE graph points, label in polar coordinatesNow we need to figure out what's going on in between these points. Remember that *r* is never negative. From θ = 0 to θ = \frac{π}{2}, the value of *r* will move from 1 to 2.PICTURE similar to polar funcs 25 From θ = \frac{π}{2} to θ = π, the value of *r* will move from 2 to 1.PICTURE similar to polar funcs 26From θ = π to θ = \frac{3π}{2}, the value of *r* will move from 1 to 0.PICTURE similar to polar funcs 27From θ = \frac{3π}{2} to θ = 2π, the value of *r* will move from 0 to 1.PICTURE similar to polar funcs 28Again, we end with a heart shape that looks nothing like the graph r = sinθ.

%The moral is that adding constants does weird things to a polar graph.

% to graph straight line in polar: $θ = ...$