Answer to Question #273226 in Analytic Geometry for Aliyah

Question #273226

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.




1
Expert's answer
2021-11-30T10:05:52-0500

1.


P1(3,135°)P_1 (-3, 135°)

Or


P1(3cos(135°),3sin(135°))P_1 (-3\cos(135\degree), -3\sin(135\degree))



P2(2,3.14/3)P_2 (2, -3.14/3)

Or


P1(2cos(3.14/3),3sin(3.14/3))P_1 (2\cos(-3.14/3), 3\sin(-3.14/3))



P2(4,405°)P_2 (4, 405\degree)

Or


P1(4cos(405°),4sin(405°))P_1 (4\cos(405\degree), 4\sin(405\degree))

2.


r=32cosθr = 3 − 2\cosθθ(rad)0π/6π/4π/3π/2r1333223\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}


θ(rad)2π/33π/45π/6πr43+23+35\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}


θ(rad)7π/65π/47π/33π/2r3+33+243\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}


θ(rad)5π/37π/411π/62πr232331\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}

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