Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 4 - Test - Page 194: 13c

Answer

$53.21^{\circ}\text {F}$

Work Step by Step

The average monthly temperature for the month of December can be found by substituting $x=12$ in the formula: $y=67.5+16.5\sin [\frac{\pi}{6}(x-4)]\\$ $y=67.5+16.5\sin [\frac{\pi}{6}(12-4)]\\$ $y=67.5+16.5\sin [\frac{\pi}{6}(8)]\\$ $y=67.5+16.5\sin [\frac{4\pi}{3}]\\$ $y=67.5+16.5(-0.8660254038)\\$ $y=67.5-14.28941916\\$ $y=53.21058084\approx53.21$ Therefore, the temperature in December is approximately $53.21^{\circ}\text{ F}$ Using the graph and locating the point when $x=12$ gives $53.211^o\text{ F}$ (refer to the graph below), which matches the answer above.
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