## Trigonometry (11th Edition) Clone

Published by Pearson

# Chapter 3 - Radian Measure and the Unit Circle - Section 3.3 The Unit Circle and Circular Functions - 3.3 Exercises - Page 125: 89a

#### Answer

The angle of elevation of the sun in the sky over New Orleans is $32.4^{\circ}$

#### Work Step by Step

Using the information from example 5: $D = -0.1425$ $\omega = 0.7854$ We can convert $30^{\circ}$ to units of radians: $L = (30^{\circ})(\frac{\pi~rad}{180^{\circ}}) = \frac{\pi}{6}~rad$ We can find $\theta$, the angle of elevation of the sun in the sky: $sin~\theta = cos~D~cos~L~cos~\omega+sin~D~sin~L$ $sin~\theta = cos~(-0.1425)~cos (\frac{\pi}{6})~cos~(0.7854)+sin~(-0.1425)~sin~(\frac{\pi}{6})$ $sin~\theta = 0.535155$ $\theta = sin^{-1}(0.535155)$ $\theta = 32.4^{\circ}$ The angle of elevation of the sun in the sky over New Orleans is $32.4^{\circ}$

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