Trigonometry (10th Edition)

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

Chapter 6 - Inverse Circular Functions and Trigonometric Equations - Section 6.3 Trigonometric Equations II - 6.3 Exercises: 50b

Answer

The least number of hours of daylight will occur on December 20th.

Work Step by Step

$h = \frac{35}{3}+\frac{7}{3}sin~\frac{2\pi~x}{365}$ The least number of hours of daylight will occur when $sin~\frac{2\pi~x}{365} = -1$. We can find $x$ when $sin~\frac{2\pi~x}{365} = -1$: $sin~\frac{2\pi~x}{365} = -1$ $\frac{2\pi~x}{365} = arcsin(-1)$ $\frac{2\pi~x}{365} = \frac{3\pi}{2}$ $x = \frac{(3)(365)}{4}$ $x = 274~days$ We can find the date that is 274 days after March 21st: March 31st: 10 days April 30th: 30 days + 10 days = 40 days May 31st: 31 days + 40 days = 71 days June 30th: 30 days + 71 days = 101 days July 31st: 31 days + 101 days = 132 days August 31st: 31 days + 132 days = 163 days September 30th: 30 days + 163 days = 193 days October 31st: 31 days + 193 days = 224 days November 30th: 30 days + 224 days = 254 days December 20th: 20 days + 254 days = 274 days The least number of hours of daylight will occur on December 20th.
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