Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 5 - Trigonometric Functions - Section 5.1 Angles and Their Measures - 5.1 Assess Your Understanding - Page 386: 33

Answer

$19^{\circ} 59^{'} 24^{"}$

Work Step by Step

RECALL: $1^{\circ} = 60^{'} \text{ and } 1^{'} = 60^{"}$ \begin{equation} \begin{split} 19.99^{\circ} &= 19^{\circ}+0.99^{\circ} \\ & = 19^{\circ} + 0.99 \times (1)^{\circ} \\ & = 19^{\circ}+0.99 \times (60)^{'} \\ & = 19^{\circ}+59.4^{'} \\ & = 19^{\circ}+59^{'}+0.4^{'} \\ & = 19^{\circ}+59^{'}+0.4 \times (1)^{'} \\ & = 19^{\circ}+59^{'}+0.4 \times (60)^{"} \\ & = 19^{\circ}+59^{'}+24^{"} \end{split} \end{equation} Thus, $19.99^{\circ} = 19^{\circ} 59^{'} 24^{"}$
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