As the moon revolves around the earth, the side that faces the earth is usually just partially illuminated by the sun. The phase
s 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, the earth, and the moon is θ(0<=θ<=360∘), then F=1/2(1−cosθ)
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)
Image of graph The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.