Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 2 - Review Exercises - Page 89: 27

Answer

1.0210339

Work Step by Step

Step 1: First, we convert the angle in decimal degrees: $78^{\circ}21'=78\frac{21}{60}^{\circ}=78.35^{\circ}$ Therefore, $\csc 78^{\circ}21'=\csc 78.35^{\circ}$. Step 2: Using the reciprocal identity $\csc\theta=\frac{1}{\sin\theta}$, $\csc 78.35=\frac{1}{\sin 78.35}$ Step 3: Now, we check to ensure that the calculator is in degree mode. Step 4: We then type $\frac{1}{\sin 78.35}$ into the calculator. Step 5: Solving, $\frac{1}{\sin 78.35}\approx1.0210339$.
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