Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 13, Trigonometric Ratios and Functions - 13.4 Evaluate Inverse Trigonometric Functions - 13.4 Exercises - Quiz for Lessons 13.3-13.4 - Page 880: 4


$\sin \theta=-\dfrac{\sqrt {153}}{51}$ $\cos \theta=-\dfrac{4 \sqrt {153}}{51}$ $\tan \theta=\dfrac{1}{4}$ $\csc \theta=-\dfrac{\sqrt {153}}{3}$ $\sec \theta=-\dfrac{\sqrt {153}}{12}$ $\cot \theta=4$

Work Step by Step

The Trigonometric Identities can be defined as: $\sin \theta=\dfrac{Opposite}{Hypotenuse}=-\dfrac{3}{\sqrt {153}}=-\dfrac{\sqrt {153}}{51}$ $\cos \theta=\dfrac{Adjacent}{Hypotenuse}=-\dfrac{12}{\sqrt {153}}=-\dfrac{4 \sqrt {153}}{51}$ $\tan \theta=\dfrac{Opposite}{Adjacent}=\dfrac{-3}{-12}=\dfrac{1}{4}$ $\csc \theta=\dfrac{Hypotenuse}{Opposite}=-\dfrac{\sqrt {153}}{3}$ $\sec \theta=\dfrac{Hypotenuse}{Adjacent}=\dfrac{-5}{4 \sqrt{153}}=-\dfrac{\sqrt {153}}{12}$ $\cot \theta=\dfrac{Adjacent}{Opposite}=\dfrac{-12}{-3}=4$
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