Calculus: Early Transcendentals (2nd Edition)

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

Chapter 1 - Functions - Review Exercises - Page 53: 48

Answer

$$\frac{\pi }{2} - \theta $$

Work Step by Step

$$\eqalign{ & {\text{From the triangle shown bellow we have that}} \cr & \sec \theta = \frac{{{\text{Hypotenuse}}}}{{{\text{Adjacent side}}}} \cr & \sec \theta = x \cr & and \cr & {\text{From the angle }}\frac{\pi }{2} - \theta \cr & \csc \left( {\frac{\pi }{2} - \theta } \right) = x \cr & \cr & {\text{Then,}} \cr & \frac{\pi }{2} - \theta = {\csc ^{ - 1}}x \cr & and\,\,\,\sec \theta = x \cr & \frac{\pi }{2} - \theta = {\csc ^{ - 1}}\left( {\sec \theta } \right) \cr & {\csc ^{ - 1}}\left( {\sec \theta } \right) = \frac{\pi }{2} - \theta \cr} $$
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