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: 32

Answer

$ 29^{\circ} 24^{'} 40^{"}$

Work Step by Step

RECALL: $1^{\circ} = 60^{'} \text{ and } 1^{'} = 60^{"}$ \begin{equation} \begin{split} 29.411^{\circ} &= 29^{\circ}+0.411^{\circ} \\ &= 29^{\circ} + 0.411 \times (1)^{\circ} \\ & = 29^{\circ} + 0.411 \times (60)^{'} \\ & = 29^{\circ} + 24.66^{'} = 29^{\circ}+24^{'}+0.66^{'} \\ & = 29^{\circ}+24^{'}+0.66 \times (1)^{'} \\ & = 29^{\circ} + 24^{'} + 0.66 \times (60)^{"} \\ & = 29^{\circ} + 24^{'} + 39.6^{"} \\ & \approx 29^{\circ} + 24^{'} + 40^{"} \end{split} \end{equation} Thus, $29.411^{\circ} = 29^{\circ} 24^{'} 40^{"}$
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