Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 4 - Section 4.3 - Right Triangle Trigonometry - Concept and Vocabulary Check - Page 560: 1

Answer

$\sin \theta =$ $\frac{a}{c}$ ; $\cos \theta =$ $\frac{b}{c}$ ; $\tan \theta =$ $\frac{a}{b}$ ; $\csc \theta =$ $\frac{c}{a}$ ; $\sec \theta =$ $\frac{c}{b}$ ; $\cot \theta =$ $\frac{b}{a}$
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Work Step by Step

Here, $a$ is length of side opposite $\theta $, $b$ is length of side adjacent to $\theta ,$ and $c$ is the length of the hypotenuse. Thus: $\begin{align} & \sin \theta =\frac{\text{opposite side}}{\text{hypotenuse}} \\ & =\frac{a}{c} \end{align}$ $\begin{align} & \cos \theta =\frac{\text{adjacent side}}{\text{hypotenuse}} \\ & =\frac{b}{c} \end{align}$ $\begin{align} & \tan \theta =\frac{\text{opposite side}}{\text{adjacent side}} \\ & =\frac{a}{b} \end{align}$ $\begin{align} & \csc \theta =\frac{\text{hypotenuse}}{\text{opposite side}} \\ & =\frac{c}{a} \end{align}$ $\begin{align} & \sec \theta =\frac{\text{hypotenuse}}{\text{adjacent side}} \\ & =\frac{c}{b} \end{align}$ $\begin{align} & \cot \theta =\frac{\text{adjacent side}}{\text{opposite side}} \\ & =\frac{b}{a} \end{align}$
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