Pre-Calc Trig

Create both a sine and cosine model for height of a passenger off of the ground for each of the following Ferris wheels.

1) customers must climb up 12 foot steps to get into the Ferris wheel (I.e) bottom of Ferris wheel is at the top of the steps
Diameter 67ft
Rotional speed 1 revolution every 80 seconds

2) customers gets into a Ferris wheel 17 feet below ground level (bottom of Ferris wheel is at that level)
Diameter 122ft
Rotional speed 1 revolution 150 seconds

My issue is that I don't know how to deal with the below and walking up steps and how to account for that when creating the functions. I just need the parameters for example
Amplitude =A
Vertical shift =K
Phase shift =h
Period =b
h(t)=acos(b(t-h))+k
h(t)=asin(b(t-h))+k

asked by Anonymous
  1. well, where is the center of the wheel above ground?
    12 + 67/2 = 45.5 = center above ground
    It does not say where the wheel starts so I will say it is at height = bottom
    now in general
    h = 45.5 + 33.5 sin( 2 pi t/T -p)
    where T is period in seconds and p is phase in radians
    Now I want it at the bottom or 12 ft when t = 0
    that means sin (argument) = -1
    or ( 2 pi t/T - p) = -pi/2
    when t = 0
    so
    p = pi/2
    so
    h = 45.5 + 33.5 sin( 2 pi t/T - pi/2)

    for the cos function, same deal but
    h = 45.5 + 33.5 cos( 2 pi t/T -p)
    now I want cos arg = -1 at t = 0
    cos = -1 when p = pi or -pi radians
    so
    h = 45.5 + 33.5 cos( 2 pi t/T -pi)

    posted by Damon

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math Algebra 2

    whobatman Please Help?! It might be a little hard but I will upvote if it's right!! The Colossus Ferris wheel debuted at the 1984 New Orleans World’s Fair. The ride is 180 ft tall, and passengers board the ride at an initial
  2. Algebra 2 Sine Function

    A power outage occurs 6 min after the ride started passengers must wait for their cage to be manually cranked into the lowest position in order to exit the ride. Sine function model: 82.5 sin 3 pi (t+0.5)+97.5 where h is the
  3. Algebra 2 ..

    1. An artist is designing triangular mirrors. Determine the number of different triangles that she can form using the given measurements. Then solve the triangles. Round to the nearest tenth. a=4.2 cm b= 5.7 cm measure angle A= 39
  4. Algebra 2....

    1. An artist is designing triangular mirrors. Determine the number of different triangles that she can form using the given measurements. Then solve the triangles. Round to the nearest tenth. a=4.2 cm b= 5.7 cm measure angle A= 39
  5. Algebra2---

    1. An artist is designing triangular mirrors. Determine the number of different triangles that she can form using the given measurements. Then solve the triangles. Round to the nearest tenth. a=4.2 cm b= 5.7 cm measure angle A= 39
  6. Geometry

    The word cosine literally means "the complement of the sine." Write a paragraph explaining how complements of sine and cosine are connected. I know that the sine and the cosine of complementary angles are the same. but how can i
  7. Math (PLEASE HELP!)

    A ferris wheel has a radius of 13 m. It rotates once every 24 seconds. A passenger gets on at the bottom of the wheel from a ramp which is one metre above ground level. a) If the height of the passenger is measured from the
  8. Math (PLEASE HELP!)

    A ferris wheel has a radius of 13 m. It rotates once every 24 seconds. A passenger gets on at the bottom of the wheel from a ramp which is one metre above ground level. a) If the height of the passenger is measured from the
  9. pre-calculus

    I have absolutely no idea even where to start. Please help! The carnival has come to town with a ferris wheel that has a radius of 30 feet. People get on when passenger compartments are at the lowest, 2 feet off the ground. The
  10. Pre Calculus 12

    Another sine/cosine question i don't get in vancouver on certain day, high tide is 20m at 2am, the next low tide is 8m at 6am, what an equation that represents height (h)of water at any time (t)since midnight) what is the height

More Similar Questions