# Chapter 2 - Quiz (Sections 2.1-2.3) - Page 71: 5

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

#### Work Step by Step

$135^{\circ}= 180^{\circ}-45^{\circ}$ The angle $135^{\circ}$ makes an angle of $45^{\circ}$ above the negative x-axis. We can let $x=-1$ and $y=1$. Then $r = \sqrt{2}$. We can find the values of the six trigonometric functions: $sin ~\theta = \frac{y}{r} = \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}$ $cos ~\theta = \frac{x}{r} = \frac{-1}{\sqrt{2}} = \frac{-\sqrt{2}}{2}$ $tan ~\theta = \frac{y}{x} = \frac{1}{-1} = -1$ $csc ~\theta = \frac{r}{y} = \frac{\sqrt{2}}{1} = \sqrt{2}$ $sec ~\theta = \frac{r}{x} = \frac{\sqrt{2}}{-1} = -\sqrt{2}$ $cot ~\theta = \frac{x}{y} = \frac{-1}{1} = -1$

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