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: 50a

Answer

On June 20th, there will be about 14 hours of daylight.

Work Step by Step

$h = \frac{35}{3}+\frac{7}{3}sin~\frac{2\pi~x}{365}$ We can find $x$ when $h=14$: $h = \frac{35}{3}+\frac{7}{3}sin~\frac{2\pi~x}{365}$ $3h = 35+7sin~\frac{2\pi~x}{365}$ $sin~\frac{2\pi~x}{365} = \frac{3h-35}{7}$ $sin~\frac{2\pi~x}{365} = \frac{(3)(14)-35}{7}$ $sin~\frac{2\pi~x}{365} = 1$ $\frac{2\pi~x}{365} = arcsin(1)$ $\frac{2\pi~x}{365} = \frac{\pi}{2}$ $x = \frac{365}{4}$ $x = 91~days$ We can find the date that is 91 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 20th: 20 days + 71 days = 91 days On June 20th, there will be about 14 hours of daylight.
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