Trigonometry (10th Edition)

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

Chapter 2 - Acute Angles and Right Triangles - Section 2.3 Finding Trigonometric Function Values Using a Calculator - 2.3 Exercises: 70b

Answer

(b) $\theta_{2}$ = 49.95$^{\circ}$

Work Step by Step

For this problem, we use the following information: $\frac{c_{1}}{c_{2}}$ = $\frac{\sin θ_{1}}{\sin θ_{2}}$ $c_{1}$ = 3 x $10^{8}$ $\frac{m}{s}$ Now, we want to express the equation in terms of $\theta_{2}$. 1. $\sin θ_{2} \times (\frac{c_{1}}{c_{2}})$ = $\sin θ_{1}$ 2. $\sin θ_{2}$ = $\sin θ_{1}$ $\times$ $(\frac{c_{2}}{c_{1}})$ 3. $\theta_{2}$ = $\sin^{-1}$( [$\sin θ_{1}$ $\times$ $(\frac{c_{2}}{c_{1}})$] ) From here, we can plug in the values to solve for $\theta_{2}$. (b) $\theta_1$ = 62$^{\circ}$ $c_2$ = 2.6 x $10^8$ $\frac{m}{s}$ $\theta_{2}$ = $\sin^{-1}$( [$\sin 62^{\circ}$ $\times$ $(\frac{2.6 x 10^8}{3 x 10^{8}})$] ) $\theta_{2}$ = 49.95$^{\circ}$
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