# Sinusoidal Word Problem Help

1. Dec 6, 2009

### Cuisine123

1. The problem statement, all variables and given/known data
A satellite is deployed from a space shuttle into an orbit which goes alternately north and south
of the equator. Its distance from the equator over time can be approximated by a sine wave. It
reaches 4500 km, its farthest point north of the equator, 15 minutes after the launch. Half an
orbit later it is 4500 km south of the equator, its farthest point south. One complete orbit takes
2 hours.

a. Find an equation of a sinusoidal function that models the distance of the satellite from
the equator.
b. How far away from the equator is the satellite 1 hour after launch?

2. Dec 6, 2009

3. Dec 7, 2009

### TheFurryGoat

You should start off with what you have:
sinusoidal function means a function off this sort: A*sin(xt+a), where a and A are constants.
The info gives you a couple of equations

$$(i)\ l(t)=Asin(xt+a)\leq4500km$$
$$(ii)\ l(t)=l(t+2h)$$
$$(iii)\ l(15min)=Asin(x*15+a)=4500km$$

4. Dec 7, 2009

### The Tutor

Assume the equator is 0, and the max/min is 4500. This is your amplitude. You can find your period by using period=2pi/k, which would equate to:

period= 360/45