| 
  • If you are citizen of an European Union member nation, you may not use this service unless you are at least 16 years old.

  • Stop wasting time looking for files and revisions! Dokkio, a new product from the PBworks team, integrates and organizes your Drive, Dropbox, Box, Slack and Gmail files. Sign up for free.

View
 

CircularFunctions

Page history last edited by PBworks 13 years, 2 months ago

Learning Objectives

 

Problem 1 of 3

 

A ferris wheel at an amusement park has riders get on at the bottom of the wheel which is 3 meters above the ground. The highest point of the ride is 21 meters above the ground and it takes 48 seconds to make a one complete revolution.

 

(a) Write two equations, one sine and one cosine, that models the height of a rider over time beginning from when they first start the ride.

(b) How long would it take a rider to pass through an angle of 2π/3 radians?

(c) How long during each revolution is a rider higher than 10 meters above the ground?

 

Solution

 

a) H(t)= 3sin[(2π/48(t+0)]+12 and H(t)= -3cos[(2π/48)(t-12)]+12

 

 

b) it would take about 9 + 48 = 57 seconds to pass through the angle of 2π/3 radians

 

 

c) 10 = 3sin[(2π/48(t)]+12

 

let [2π/48(t)]=x

 

10=3sinx+12

-2=3sinx

sinx=-2/3

 

(48/2π)[2π/48(t)]= -2/3(48/2π)

t=-2/3(48/2π)

 

^^ i think..need my notes and calculator

 

 

still working on this...don't take..hehe sorry got no calculator on me right now..ill be back tomorrow =D

 

 

 

Problem 2 of 3

 

Determine the general solution algebraically. (Solve over the set of real numbers and write your answer accurate to at least 3 decimal places.)

3cos2 x = 8cos x - 4

 

Solution

 

 

 

Problem 3 of 3

 

A sinusoidal curve has a minimum point at (-π/3, -5) and the closest maximum point to the right is (π/6, 3).

 

(a) Determine an equation of this curve.

(b) Sketch the graph.

 

Solution

Comments (0)

You don't have permission to comment on this page.