Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 5 - Section 5.2 - Sum and Difference Formulas - Exercise Set - Page 671: 95


The given statement makes sense.

Work Step by Step

The given statement makes complete sense because the exact value for the trigonometric functions of $60{}^\circ \And 45{}^\circ $ can be calculated with the sum formula to calculate $\sin {{105}^{\circ }}$ $\begin{align} & \sin 105{}^\circ =\sin \left( 60{}^\circ +45{}^\circ \right) \\ & =\sin 60{}^\circ \cos 45{}^\circ +\cos 60{}^\circ \sin 45{}^\circ \\ & =\frac{\sqrt{3}}{2}\cdot \frac{1}{\sqrt{2}}+\frac{1}{2}\cdot \frac{1}{\sqrt{2}} \end{align}$ Then, further solving the equation, the result will be: $\begin{align} & \sin 105{}^\circ =\frac{\sqrt{2}\left( \sqrt{3}+1 \right)}{4} \\ & =\frac{1.4142\left( 1.7320+1 \right)}{4} \\ & =0.9656 \end{align}$ Thus, the given statement makes sense.
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