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: 11


$sin~x=\frac{2\sqrt {13}}{13}$ $cos~x=\frac{3\sqrt {13}}{13}$ $tan~x=\frac{2}{3}$ $cot~x=\frac{3}{2}$ $sec~x=\frac{\sqrt {13}}{3}$ $csc~x=\frac{\sqrt {13}}{2}$

Work Step by Step

$cos~x\gt0$ $tan~x=\frac{sin~x}{cos~x}\gt0$ We can conclude that: $sin~x\gt0$ $cot~x=\frac{1}{tan~x}\gt0$ $sec~x=\frac{1}{cos~x}\gt0$ $csc~x=\frac{1}{sin~x}\gt0$ $sec^2x=tan^2x+1=\frac{4}{9}+1=\frac{13}{9}$ $sec~x=\frac{\sqrt {13}}{3}$ $cos~x=\frac{1}{sec~x}=\frac{3}{\sqrt {13}}=\frac{3\sqrt {13}}{13}$ $cot~x=\frac{1}{tan~x}=\frac{3}{2}$ $csc^2x=cot^2x+1=\frac{9}{4}+1=\frac{13}{4}$ $csc~x=\frac{\sqrt {13}}{2}$ $sin~x=\frac{1}{csc~x}=\frac{2}{\sqrt {13}}=\frac{2\sqrt {13}}{13}$
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