Question

the sun always illuminates half of the moon's surface, except during a lunar eclipse. the illuminated portion of tge moon visible from earth varies as it revolves around the earth resulting in the phases of the moon. the period from a full moon to a new moon and back to a full moon is called a synodic month and is 29 days, 12 hours, and 44.05 minutes long. write a sine function that models the fraction of the moon's surface which is seen to be illuminated during a synodic month as a function of the number of days, d, after a full moon.

Answer 1

We are given the period of the function which is
29 days, 12 hours, and 44.05 minutes or 29.5306 days
If we let
s be the fraction of the moon's surface seen
M be half of the moon's surface


The sine function is
s = M sin bθ

T = 2 π /b
b  = 2π / 29.5306

s = M sin 2πθ / 29.5306