# Polar Curves Worksheet

Polar Curves Worksheet
• Page 1
1.
Find the area of the region bounded by the graph $r$2 = 2cos θ and between the rays θ = - $\frac{\pi }{6}$ and $\frac{\pi }{4}$.
 a. $\sqrt{2}+1$ square units b. $\frac{\sqrt{2}-1}{2}$ square units c. $\frac{\sqrt{2}+1}{2}$ square units d. $\frac{\sqrt{2}+\sqrt{3}}{2}$ square units

2.
Find the arc length of the curve $r$ = 1 - sin $\theta$, 0 ≤ $\theta$$\frac{\pi }{2}$.
 a. 2$\sqrt{2}\left(\sqrt{2}-1\right)$ units b. 2$\sqrt{2}\left(\sqrt{2}+1\right)$ units c. $\sqrt{2}\left(\sqrt{2}+1\right)$ units d. $\sqrt{2}\left(\sqrt{2}-1\right)$ units

3.
Find the arc length of the curve $r$ = 1 - cos $\theta$, 0 ≤ $\theta$ ≤ π.
 a. 2 units b. 8 units c. 4 units d. 16 units

4.
Find the arc length of the curve $r$ = sec $\theta$, 0 ≤ $\theta$$\frac{\pi }{3}$.
 a. $\frac{\sqrt{3}}{3}$ units b. $\frac{\sqrt{3}}{6}$ units c. $\sqrt{3}$ units d. 2$\sqrt{3}$ units

Find the arc length of the curve $r$ = sin $\theta$ + cos $\theta$, 0 ≤ $\theta$$\frac{\pi }{4}$.
 a. $\frac{\sqrt{2}\pi }{2}$ units b. $\frac{\sqrt{2}\pi }{8}$ units c. $\sqrt{2}\pi$ units d. $\frac{\sqrt{2}\pi }{4}$ units