Identifying Key Features
Writing Equations from Words
Writing Equations from Graphs
Ferris Wheel
Unit Circle
100
The amplitude of y=-5cos(4(x-pi))-7
What is 5?
100
The equation for cos that has a phase shift left 5, vertical shift down 6, amplitude of 1, and a period of 2pi .
What is y = cos(x+5) - 6?
100
y = sin(2x)-1 matches to...
What is C?
100
A Ferris wheel has a diameter of 30 m with its center 18 m above the ground. It makes one complete rotation every 60 seconds. Assume the rider starts at the lowest point.
Sketch a graph modeling this situation.
What is
100
Use your unit circle to find the value(s) of
theta
in the interval [0,2pi] such that
cos(theta)=1/2
What is
theta = pi/3, (5pi)/3
200
The period of y=-5cos(4(x-pi))-7
What is
pi/2?
200
The equation for cos that has an amplitude of 3 and a period of 8pi (no vertical or phase shift)
What is
y=3cos(1/4x)?
200
y=2cos(x+pi/4)+1
What is A?
200
A Ferris wheel has a diameter of 30 m with its center 18 m above the ground. It makes one complete rotation every 60 seconds. Assume the rider starts at the lowest point.
Write a function expressing the height above the ground in terms of seconds since the ride started.
What is
h=-15cos(pi/30t)+18
200
Use your unit circle to find the value(s) of
theta
in the interval [0,2pi] such that
sin(theta)=1
What is
theta=pi/2
300
The phase shift of y=-5cos(4(x-pi))-7 (give direction too)
What is right
pi
300
The equation for sin that has an amplitude of 2 and a period of pi/2 (no vertical or phase shift)
What is y = 2sin(4x)?
300
y = 2sin(2x)-1
What is F?
300
A Ferris wheel has a diameter of 30 m with its center 18 m above the ground. It makes one complete rotation every 60 seconds. Assume the rider starts at the lowest point.
Is the rider moving up or down when the ride starts?
What is up?
300
Use your unit circle to find the value(s) of
theta
in the interval [0,2pi] such that
sec(theta)=-2
What is
theta=(2pi)/3, (4pi)/3
400
The vertical shift of y=-5cos(4(x-pi))-7 (give direction too)
What is down 7?
400
The equation for cos that has an amplitude of 4, a phase shift right pi/6 , vertical shift down 10 and a period of 2pi .
What is
y=4cos(x-pi/6)-10?
400
y=2sin(x+pi/4)+1
What is G?
400
A Ferris wheel has a diameter of 30 m with its center 18 m above the ground. It makes one complete rotation every 60 seconds. Assume the rider starts at the lowest point.
How high above the ground are you 10 seconds after the ride starts? (no calculator)
What is 10.5 meters?
400
Use your unit circle to find the value(s) of
theta
in the interval [0,2pi] such that
tan(theta)=sqrt(3)/3
What is
theta=pi/6, (7pi)/6
500
Identify the amplitude, period, phase shift and vertical shift of y=5sin(1/5(x+pi/6))+7
What is an amplitude of 5, period of 10
pi
, vertical shift up 7 and phase shift left
pi/6
500
The equation for sin that has an amplitude of 1/2, a reflection over the x-axis, a period of pi/10 ,a vertical shift up 5 and a phase shift left pi/3 .
What is -1/2sin(20(x+pi/3))+5
500
y=cos(x+pi/2)-1
What is B?
500
A Ferris wheel has a diameter of 30 m with its center 18 m above the ground. It makes one complete rotation every 60 seconds. Assume the rider starts at the lowest point.
The first time that you will be 30 meters above the ground is (calculator allowed)
What is 6.144 seconds?
500
Use your unit circle to find the value(s) of
theta
in the interval [0,2pi] such that
cot(theta)= Undefined
What is theta = 0, pi, 2pi