Modeling Satellite Orbit with Sinusoidal Functions

[Cuisine123]

Homework Statement

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?

 

[Cuisine123]

If anyone has any clue to this question, please help, because I really need it soon.

 

[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

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

 

[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
period=8 (I believe your working in radians?)

I might be wrong about the period, but it's pretty easy to go on from there. To do question #2, just substitute 60 into time.