## Trigonometry (11th Edition) Clone

Published by Pearson

# Chapter 1 - Test - Page 46: 14

#### Answer

$sin ~\theta = -\frac{7}{\sqrt{53}}$ $cos ~\theta =\frac{2}{\sqrt{53}}$ $tan ~\theta =-\frac{7}{2}$ $csc ~\theta = -\frac{\sqrt{53}}{7}$ $sec ~\theta = \frac{\sqrt{53}}{2}$ $cot ~\theta = -\frac{2}{7}$

#### Work Step by Step

$x = 2,$ $y = -7$ We can form a triangle with the three points $(0,0),(2,0),$ and $(2,-7)$ We can find the length $r$ of the hypotenuse: $r = \sqrt{(2)^2+(-7)^2} = \sqrt{53}$ Note that the trigonometric values of $\theta$ are equal to the trigonometric values of the angle $\theta-360^{\circ}$ We can find the values of the six trigonometric functions: $sin ~\theta = \frac{y}{r} = -\frac{7}{\sqrt{53}}$ $cos ~\theta = \frac{x}{r} = \frac{2}{\sqrt{53}}$ $tan ~\theta = \frac{y}{x} = -\frac{7}{2}$ $csc ~\theta = \frac{r}{y} = -\frac{\sqrt{53}}{7}$ $sec ~\theta = \frac{r}{x} = \frac{\sqrt{53}}{2}$ $cot ~\theta = \frac{x}{y} = -\frac{2}{7}$

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