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: 27

Answer

\[\begin{gathered} we\,obtained\,zero\,in\,denominator\,,\,\ so\, the\, expression\, \hfill \\ is\,undefined. \hfill \\ \end{gathered} \]

Work Step by Step

\[\begin{gathered} Using\,\,definition\,.{\text{ of }}\,\,\sec x \hfill \\ \hfill \\ \sec \,\,\left( {\frac{{5\pi }}{2}} \right) = \frac{1}{{\cos \,\left( {\frac{{5\pi }}{2}} \right)}} \hfill \\ \hfill \\ the\,\,period\,of\,cosine\,function\,is\,2\pi \, \hfill \\ \hfill \\ \frac{1}{{\cos \,\left( {\frac{{5\pi }}{2}} \right)}} = \frac{1}{{\cos \,\,\left( {\frac{{5\pi }}{2} - 2\pi } \right)}} = \frac{1}{{\cos \,\left( {\frac{\pi }{2}} \right)}} = \frac{1}{0} \hfill \\ \hfill \\ since\,\,we\,obtained\,zero\,in\,denominator\,,\,\exp ression\, \hfill \\ is\,undefined. \hfill \\ \hfill \\ \end{gathered} \]
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