Answer to Question #273226 in Analytic Geometry for Aliyah

Question

Exercise 6.1

Plot the following points:

1.P1 (-3, 135°)

P2 (2, -3.14/3)

P3 (4, 405°)

   Then graph

2.Sketch the graph of r = 3 − 2cosθ.

Answer 1

1.

$$P_1 (-3, 135°)$$

Or

$$P_1 (-3\cos(135\degree), -3\sin(135\degree))$$

$$P_2 (2, -3.14/3)$$

Or

$$P_1 (2\cos(-3.14/3), 3\sin(-3.14/3))$$

$$P_2 (4, 405\degree)$$

Or

$$P_1 (4\cos(405\degree), 4\sin(405\degree))$$

2.

$$r = 3 − 2\cosθ$$ $$\def\arraystretch{1.5} \begin{array}{c:c:c:c:c:c} \theta (rad) & 0 & \pi/6 & \pi/4 & \pi/3 & \pi/2 \\ \hline r & 1 & 3-\sqrt{3} & 3-\sqrt{2} & 2 & 3 \\ \end{array}$$

$$\def\arraystretch{1.5} \begin{array}{c:c:c:c:c} \theta (rad) & 2\pi/3 & 3\pi/4 & 5\pi/6 & \pi \\ \hline r & 4 & 3+\sqrt{2} & 3+\sqrt{3} & 5 \\ \end{array}$$

$$\def\arraystretch{1.5} \begin{array}{c:c:c:c:c} \theta (rad) & 7\pi/6 & 5\pi/4 & 7\pi/3 & 3\pi/2 \\ \hline r & 3+\sqrt{3} & 3+\sqrt{2} & 4 & 3 \\ \end{array}$$

$$\def\arraystretch{1.5} \begin{array}{c:c:c:c:c} \theta (rad) & 5\pi/3 & 7\pi/4 & 11\pi/6 & 2\pi \\ \hline r & 2 & 3-\sqrt{2} & 3-\sqrt{3} & 1 \\ \end{array}$$