Question

- Shelly observes the moon outside her window each night. The percentage of the moon she can see

+50 where P is the percent of
2π
28
can be modeled by the sinusoidal function given by P = 50 sin
the moon that is visible and t is the day. She started observing on June 7th which she represents as
t = 0.

c. On what day will there be a Full Moon?
d. On what day will there be a New Moon? (New Moon refers to the day when the moon is not visible)

Answer 1

Based on the sinusoidal function modeling Shelly's observations, the full moon will occur on June 21st, and the new moon will occur on June 28th.

Step-by-step explanation:

Shelly's observations of the moon's phases can be modeled using a sinusoidal function. Since the moon goes through its phases over 29.5 days, we can determine when a full moon and a new moon will occur based on this cycle.

For a full moon, we need the sine function to be at its maximum, which is when sin(2πt/28) = 1. Solving for t, we have t = (28/2π) * (1/2)π = 14 days after her observation starts. As she began observing on June 7th, the full moon will occur 14 days later, which is June 21st.

For a new moon, we need the sine function to be at its minimum, when sin(2πt/28) = -1. Solving for t in the same manner gives us t = (28/2π) * (3/2)π = 21 days after her observations begin. Adding 21 days to June 7th, the new moon will occur on June 28th.