# Chapter 2 - Quiz (Sections 2.1-2.3) - Page 71: 6

$sin ~\theta = -\frac{1}{2}$ $cos ~\theta = -\frac{\sqrt{3}}{2}$ $tan ~\theta = \frac{\sqrt{3}}{3}$ $csc ~\theta = -2$ $sec ~\theta = -\frac{2\sqrt{3}}{3}$ $cot ~\theta = \sqrt{3}$

#### Work Step by Step

$-150^{\circ}+360^{\circ} = 210^{\circ} = 180^{\circ}+30^{\circ}$ The angle $-150^{\circ}$ makes an angle of $30^{\circ}$ below the negative x-axis. We can let $x=-\sqrt{3}$ and $y=-1$. Then $r = 2$. We can find the values of the six trigonometric functions: $sin ~\theta = \frac{y}{r} = \frac{-1}{2}$ $cos ~\theta = \frac{x}{r} = \frac{-\sqrt{3}}{2}$ $tan ~\theta = \frac{y}{x} = \frac{-1}{-\sqrt{3}} = \frac{\sqrt{3}}{3}$ $csc ~\theta = \frac{r}{y} = \frac{2}{-1} = -2$ $sec ~\theta = \frac{r}{x} = \frac{2}{-\sqrt{3}} = -\frac{2\sqrt{3}}{3}$ $cot ~\theta = \frac{x}{y} = \frac{-\sqrt{3}}{-1} = \sqrt{3}$

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