Trigonometry (10th Edition)

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

Chapter 1 - Trigonometric Functions - Section 1.1 Angles - 1.1 Exercises: 137

Answer

4 seconds

Work Step by Step

1. The clue here is to figure out that telescope is going to have the same rate of rotation as the earth that is simply $360^{\circ}/24hours$ 2. Don't get confused by minutes of the time and the minutes of a degree. We are going to convert degrees to minutes (') $\frac{360^{\circ}}{24hr}\times\frac{69'}{1^{\circ}}=21600'/24hr$ 3. Let's reduce the number $\frac{21600'}{24h}=\frac{900'}{1hr}$ 4. We need to get down to one minute of a degree, so let's start applying conversation factors and reducing $\frac{900'}{1hr}\times \frac{1hr}{60min}$= 15'/min 5. Finally, how much does it take to go through one minute of rotation $\frac{15'}{60sec} =\frac{1'}{4sec}$
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