Back40–41. {Use of Tech} Slopes of tangent lines
b. Find the slope of the lines tangent to the curve at the origin (when relevant).
r =3 − 6 cos θ
85–87. Grazing goat problems Consider the following sequence of problems related to grazing goats tied to a rope. (See the Guided Project Grazing goat problems.)
A circular corral of unit radius is enclosed by a fence. A goat is outside the corral and tied to the fence with a rope of length 0≤a ≤ π (see figure). What is the area of the region (outside the corral) that the goat can reach?