Calculus- Early Transcendentals, 2021a

410 Polar Coordinates, Parametric Equations
(a) r = √ sinθ
(b) r = 2 + cosθ
(c) r = secθ,π/6 ≤ θ ≤ π/3
(d) r = cosθ,0≤ θ ≤ π/3
(e) r = 2acosθ,a > 0
(f) r = 4 + 3sinθ
Exercise 11.3.2 Find the area inside the loop formed by r = tan(θ/2).
Exercise 11.3.3 Find the area inside one loop of r = cos(3θ).
Exercise 11.3.4 Find the area inside one loop of r = sin 2 θ.
Exercise 11.3.5 Find the area inside the small loop of r =(1/2)+cosθ.
Exercise 11.3.6 Find the area inside r =(1/2)+cosθ, including the area inside the small loop.
Exercise 11.3.7 Find the area inside one loop of r 2 = cos(2θ).
Exercise 11.3.8 Find the area enclosed by r = tanθ and r = cscθ √
2
.
Exercise 11.3.9 Find the area inside r = 2cosθ and outside r = 1.
Exercise 11.3.10 Find the area inside r = 2sinθ and above the line r =(3/2)cscθ.
Exercise 11.3.11 Find the area inside r = θ, 0 ≤ θ ≤ 2π.
Exercise 11.3.12 Find the area inside r = √ θ, 0 ≤ θ ≤ 2π.
Exercise 11.3.13 Find the area inside both r = √ 3cosθ and r = sinθ.
Exercise 11.3.14 Find the area inside both r = 1 − cosθ and r = cosθ.
Exercise 11.3.15 The center of a circle of radius 1 is on the circumference of a circle of radius 2. Find
the area of the region inside both circles.
Exercise 11.3.16 Find the shaded area in figure 11.10. Thecurveisr= θ, 0 ≤ θ ≤ 3π.