Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 1 - Functions - 1.4 Trigonometric Functions and Their Inverse - 1.4 Exercises - Page 47: 5

Answer

\[\begin{gathered} {\text{1)}}\,\,\,\,\,\,{\sin ^2}\theta + {\cos ^2}\theta = 1 \hfill \\ {\text{2)}}\,\,\,\,\,\,1 + {\cot ^2}\theta = {\csc ^2}\theta \hfill \\ {\text{3)}}\,\,\,\,\,\,{\tan ^2}\theta + 1 = {\sec ^2}\theta \hfill \\ \end{gathered} \]

Work Step by Step

\[\begin{gathered} {\text{The three Pythagorean identities are:}}\,\,\,\left( {{\text{See page 41}}} \right) \hfill \\ {\text{1)}}\,\,\,\,\,\,{\sin ^2}\theta + {\cos ^2}\theta = 1 \hfill \\ {\text{2)}}\,\,\,\,\,\,1 + {\cot ^2}\theta = {\csc ^2}\theta \hfill \\ {\text{3)}}\,\,\,\,\,\,{\tan ^2}\theta + 1 = {\sec ^2}\theta \hfill \\ \end{gathered} \]
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