Question

1. The moon's distance from Earth varies in a periodic way that can be modeled by a trigonometric function. When the moon is at its perigee (closest point to Earth), it's about 363,000 km away. When it's at its apogee (farthest point from Earth), it's about 406,000 away. The moon's apogees occur 27.3 days apart. The moon will reach its apogee on January 222, 2016. Find the formula of the trigonometric function that models the distance D between Earth and the moon t days after January 1, 2016.

Answer 1

The trigonometric model of the distance between Earth and the Moon is:

Where:

A- Apogee, measured in kilometers.

∆A - Amplitude, measured in kilometers.

- Angular frequency, measured in radians.

- Phase angle, measured in radians.

t - Time, measured in days.

Now,The expression is: