Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 7 - 7.1 - Using Fundamental Identities - 7.1 Exercises - Page 513: 12


$sin~x=-\frac{4\sqrt {65}}{65}$ $cos~x=-\frac{7\sqrt {65}}{65}$ $tan~x=\frac{4}{7}$ $cot~x=\frac{7}{4}$ $sec~x=-\frac{\sqrt {65}}{7}$ $csc~x=-\frac{\sqrt {65}}{4}$

Work Step by Step

$sin~x\lt0$ $cot~x=\frac{cos~x}{sin~x}\gt0$ We can conclude that: $cos~x\lt0$ $tan~x=\frac{1}{cot~x}\gt0$ $sec~x=\frac{1}{cos~x}\lt0$ $csc~x=\frac{1}{sin~x}\lt0$ $csc^2x=cot^2x+1=\frac{49}{16}+1=\frac{65}{16}$ $csc~x=-\frac{\sqrt {65}}{4}$ $sin~x=\frac{1}{csc~x}=-\frac{4}{\sqrt {65}}=-\frac{4\sqrt {65}}{65}$ $tan~x=\frac{1}{cot~x}=\frac{4}{7}$ $sec^2x=tan^2x+1=\frac{16}{49}+1=\frac{65}{49}$ $sec~x=-\frac{\sqrt {65}}{7}$ $cos~x=\frac{1}{sec~x}=-\frac{7}{\sqrt {65}}=-\frac{7\sqrt {65}}{65}$
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