Phases of the Moon As the moon revolves around the earth, the side that faces the earth is usually just partially illuminated by the sun. The phases of the moon describe how much of the surface appears to be in sunlight. An astronomical measure of phase is given by the fraction F of the lunar disc that is lit. When the angle between the sun, earth, and moon is θ (0 ≤ θ ≤ 360°), then
Determine the angles θ that correspond to the following phases:
- (a) F = 0 (new moon)
- (b) F = 0.25 (a crescent moon)
- (c) F = 0.5 (first or last quarter)
- (d) F = 1 (full moon)
(a)
The value of
Answer to Problem 59E
The value of
Explanation of Solution
Given:
The astronomical measure of phase of the lunar disc that is lit is
Calculation:
Substitute the value
That is,
Thus, the value of
(b)
The value of
Answer to Problem 59E
The values of
Explanation of Solution
Substitute the value
Note that, cosine function is positive in the first and fourth quadrants and its period is
Therefore, the other angle is obtained as follows.
Thus, the values of
(c)
The value of
Answer to Problem 59E
The values of
Explanation of Solution
Substitute the value
That is,
Cosine function is a periodic function with period
Note that,
Thus, the values of
(d)
The value of
Answer to Problem 59E
The value of
Explanation of Solution
Substitute the value
Thus, the value of
Chapter 7 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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