# Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.5 Polar Equations and Graphs - 8.5 Exercises - Page 394: 21

$(3, \frac{5\pi}{3})$ (a) We can see the point plotted on the graph below. (b) We can write two other pairs of polar coordinates for this point: $(3, -\frac{\pi}{3})$ $(-3, \frac{2\pi}{3})$ (c) $(x,y) = (\frac{3}{2}, -\frac{3\sqrt{3}}{2})$

#### Work Step by Step

$(3, \frac{5\pi}{3})$ (a) We can see the point plotted on the graph below. (b) We can write two other pairs of polar coordinates for this point: $(3, -\frac{\pi}{3})$ $(-3, \frac{2\pi}{3})$ (c) We can find the rectangular coordinates: $r = 3$ and $\theta = \frac{5\pi}{3}$ $(x,y) = (r~cos~\theta, r~sin~\theta)$ $(x,y) = (3~cos~\frac{5\pi}{3}, 3~sin~\frac{5\pi}{3})$ $(x,y) = (\frac{3}{2}, -\frac{3\sqrt{3}}{2})$

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