trig application problem?

Question

I need help writing an equation to model a sine wave on a graph. If you could explain how to get the equation, that would be great. I have a quiz coming up and I need to learn how to put these together.

Assume that a satellite launched from Cape Canaveral eventually has an orbit of 2 hours. It reaches 5600 km, its farthest point north of the equator, 45 minutes after the launch and begins its orbit. One hour later, it is 5600 km south of the equator, its farthest point south. 

Thanks!

Paula · Accepted Answer

First decide your units. Let's say x is in hours, y is in km (+ for north, - for south)

A general sine function has this form:

y = A sin(2(pi)x/B + C) + D

"has an orbit of 2 hours" ... that means the period of the function will be 2 (hours). So B=2.

It varies from 5600 to -5600. So it centres at 0, so D=0. An ordinary sine function varies from +1 to -1, so we want to multiply by 5600. So A = 5600.

So far we have
y = 5600 sin((pi)x + C)
All we need to find is C. The furthest point is at x=3/4 (45 minutes is 3/4 of an hour). So we want
5600 sin((pi)(3/4) + C) = 5600
=> sin((pi)(3/4) + C) = 1
 (but sin x = 1 when x = pi/2, so...)
=> (pi)(3/4) + C = pi/2
=> C = -pi/4

Anonymous · Answer

Draw it out. It makes it much less complicated. Draw the slide and ladder as a ideal triangle. One leg is 5. One approach is 32 stages. Your staring at in the process the slide, it incredibly is the hypotenuse. To clean up this disaster, you could use the cosine place, that is adjacent over hypotenuse. Your equation sounds like this: cos 32 = 5/x multiply each area by using x and divide in the process the cos 32. your equation will could desire to like this now: x = 5/cos32 purely punch that into your calculator and you get the era of the hypotenuse. then you definately make the main of the pythagorean theorem or one extra trig place to be sure the era of the perfect area. this could could desire to supply help to do no longer forget the thank you to connected matters: SOH CAH TOA sine = opposite/hypotenuse cosine = adjacent/hypotenuse tangent = opposite/adjacent desire that's assisting :)

trig application problem?

2 Answers