# Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.5 Polar Equations and Graphs - 8.5 Exercises - Page 394: 32

(a) We can see the point plotted on the graph below. (b) We can write two pairs of polar coordinates for this point: $(1, 210^{\circ})$ $(-1, 30^{\circ})$

#### Work Step by Step

$(\frac{-\sqrt{3}}{2}, -\frac{1}{2})$ (a) We can see the point plotted on the graph below. (b) $r = \sqrt{(\frac{-\sqrt{3}}{{2}})^2+(-\frac{1}{2})^2} = 1$ We can find the angle $\phi$ below the negative x-axis: $tan~\phi = \frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}$ $\phi = arctan(\frac{1}{\sqrt{3}})$ $\phi = 30^{\circ}$ We can write two pairs of polar coordinates for this point: $(1, 210^{\circ})$ $(-1, 30^{\circ})$

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