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: 45

Answer

\[\,\,\theta = 0,\pi ,\frac{\pi }{2},\frac{{3\pi }}{2}\,\,\]

Work Step by Step

\[\begin{gathered} \sin \theta \cos \theta = 0\, \hfill \\ \, \hfill \\ so\,\,\sin \theta = 0\,\,or\,\,\cos \theta = 0 \hfill \\ \hfill \\ Using\,\,figure\,\,1.63\,\,and\,\,the\,definition\,of\,\,sine\,and\,\,cosine \hfill \\ \,functions\,we\,obtain. \hfill \\ \hfill \\ If\,\,\sin \,\theta = 0\,\,\,then\,\,\theta = 0,\pi \hfill \\ \hfill \\ If\,\,\cos \theta \, = 0\,\,\,\,Then\,\,\,\,\theta = \frac{\pi }{2}\,,\,\frac{{3\pi }}{2} \hfill \\ \hfill \\ {\text{Therefore}} \hfill \\ \hfill \\ All\,solutions\,\,are\,\,:\,\,\,\theta = 0,\pi ,\frac{\pi }{2},\frac{{3\pi }}{2}\,\, \hfill \\ \end{gathered} \]
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