Tonight a full moon is out. The percentage of moon that is visible, v, according to the number of days from now, d, is modelled by the equation v(d)=0.5cos(2pid/29.5)+0.5. a) How many days is there until the new moon (no moon visible)?

b) Including tonight, how many full moons will there be in the next 100 days?

c) How many days will it be until there are five full moons, including tonight's?

d) Without using trigonometric ratios, find a simple equation that tells how many days away the next x full moons are. Why can the equation be so simple and consistent?