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.

Question

Mathematics

Sterling Quinn

17 June, 13:20

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.

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Huerta · 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 b θ

T = 2 π / b

b = 2π / 29.5306

s = M sin 2πθ / 29.5306