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

Question

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 the fraction F is given by the formula below. Determine the angles θ that correspond to the following phases. (If there are any unused answer boxes, enter NONE in the last boxes.)
F=1/2(1-cos(theta))
a. F=0
b. F=0.25
c. F= 0.5
d. F=1