Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 5 - Trigonometric Functions - Section 5.2 Trigonometric Functions: Unit Circle Approach - 5.2 Assess Your Understanding - Page 403: 83

Answer

1. $sin(\theta)= \frac{3}{5}$. 2. $cos(\theta)= \frac{4}{5}$. 3. $tan(\theta)= \frac{3}{4}$. 4. $cot(\theta)= \frac{4}{3}$. 5. $sec(\theta)= \frac{5}{4}$. 6. $csc(\theta)= \frac{5}{3}$.

Work Step by Step

Given point $(\frac{1}{3},\frac{1}{4})$, we have $x=\frac{1}{3}, y=\frac{1}{4}, r=\sqrt {(\frac{1}{3})^2+(\frac{1}{4})^2}=\frac{5}{12}$, we have: 1. $sin(\theta)= \frac{y}{r}= \frac{\frac{1}{4}}{\frac{5}{12}}=\frac{3}{5}$. 2. $cos(\theta)= \frac{x}{r}= \frac{\frac{1}{3}}{\frac{5}{12}}=\frac{4}{5}$. 3. $tan(\theta)= \frac{y}{x}=\frac{\frac{1}{4}}{\frac{1}{3}}=\frac{3}{4}$. 4. $cot(\theta)=\frac{1}{tan(\theta)}=\frac{4}{3}$. 5. $sec(\theta)=\frac{1}{cos(\theta)}=\frac{5}{4}$. 6. $csc(\theta)=\frac{1}{sin(\theta)}=\frac{5}{3}$.
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