Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 1 - Trigonometric Functions - Section 1.4 Using the Definitions of the Trigonometric Functions - 1.4 Exercises: 72

Answer

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

Work Step by Step

1. Angle in III quadrant, therefore x and y are neagtive $x=-1$ and $y=-\sqrt 3$ 2. Calculate r using distance formula: $r=\sqrt {(-1)^{2}+(-\sqrt 3)^{2}} =\sqrt {4}=2$ 3. Plug the values into the expression $\sin\theta=\frac{y}{r}=\frac{-\sqrt 3}{2}$ $\cos\theta=\frac{x}{r}=\frac{-1}{2}$ $\tan\theta=\frac{y}{x}=\frac{-\sqrt 3 }{-1}=\sqrt 3$ $\cot\theta=\frac{x}{y}=\frac{-1}{-\sqrt 3}=\frac{\sqrt 3}{3}$ $\sec\theta=\frac{r}{x}=\frac{2}{-1}=-2$ $\csc\theta=\frac{r}{y}=\frac{2}{-\sqrt 3}=\frac{-2\sqrt 3}{3}$
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