Formulas
Key Features
Graphs
Applications
Vocabulary
Modeling
100
y=|max-min|/2
What is the formula for finding amplitude?
100
Half the distance between the max and min.
What is the amplitude?
100
The average depth of water per day is____.
What is 4 feet deep?
100
A Ferris wheel has a max height of 90 ft and min of 10 ft. The amplitude is __________.
What is 40 ft?
100
Define amplitude.
What is vertical distance from the midline to the max or min?
100
The spring is pulled 3 feet downward and released. The object begins oscillating and completes one full cycle every 2 seconds.
The best model for this situation, with no phase shift, is a __________ function.
What is a negative cosine function?
200
y = (max + min)/2
What is the formula for finding midline?
200
The average of all of the y values.
What is the midline?
200
This is the period.
What is 30 seconds?
200
In a town in Alaska, daylight varies from a minimum of 4 hours to a maximum of 20 hours in a calendar year. The average hours of daylight in a year is _______. This would be represented on a graph as the ________________.
What is 12 hours? What is the midline?
200
Define midline.
What is the average of all the y-values? OR The equilibrium line that the graph oscillates around? OR the horizontal line halfway between the maximum and the minimum?
200
Find the average water depth (midline) and the maximum rise/fall in depth (amplitude).
What is average depth at 7.5 feet and the depth rises and falls 1.5 feet in either direction?
300
(2pi)/|b|
What is the formula for finding period?
300
The measure of the horizontal distance for one full cycle.
What is the period?
300
This is the period.
What is 12 hours?
300
A bike tire rotates at 80 rpm. The period for one rotation in seconds is ___________.
What is 3/4 of a second or 0.75 seconds?
300
Define period.
What is the horizontal distance it takes to complete one full cycle of a repeating pattern?
300
This is the amplitude, midline, and period for a ride on this ferris wheel. 
What is amplitude is 18 ft, midline is y= 24 ft, and period is 30 seconds?
400
(2pi)/(period)
What is the formula for finding frequency (b)?
400
In most real-world sinusoidal models, what does the x-axis represent?
What is time?
400
This is the radius of the ferris wheel modeled below.
What is 20 ft?
400
A Ferris wheel has 12 equally spaced cars, so adjacent cars are 30° apart. The loading platform is positioned so that the lowest point of the wheel is exactly halfway between two cars. If a rider starts in car 1 (the car immediately to the left of the lowest point), the phase shift (in degrees) of the sinusoidal model measured from the lowest point is _______.
What is 15 degrees?
400
Define frequency (b).
What is the number of cycles over a given period of time or interval?
400
Write an equation for a ride on this ferris wheel so there is no phase shift.
What is
y=-18sin(pi/15x)+24?
500
Given the function in the form:
f(x)=Acos(Bx-C)+D
The phase shift would be found by
What is dividing C by B?
C/B
500
A sinusoidal function has a maximum value of 18 and a minimum value of 6. One full cycle occurs from x=2 to x=10.
Give the amplitude, period, and midline.
What is amplitude is 6, period is 8, and midline is 12.
500
Give the amplitude, period, and midline.
What is the amplitude is 2 ft, period is
12 hours
, and Midline is
y=12?
500
Jason’s blood pressure is currently 120/65 mmHg, and his heart rate is 75 beats per minute. As his heart beats, his blood pressure rises from its lowest value to its highest value and then returns to its lowest value once every beat.
If you model his blood pressure as a function of time, what is the length of one period?
What is 4/5 of a second or 0.8 seconds?
500
Define phase shift.
What is the horizontal shift of the beginning of a cycle left or right from its original position?
500
A bike rider notices that the height of the air valve on his front tire changes in a repeating pattern as the wheel rotates.
At its lowest point, the valve is 2 inches above the ground, and at its highest point, it is 28 inches above the ground. The wheel completes one full rotation every 2 seconds.
Let x represent time in seconds, and let y represent the height of the valve above the ground in inches.
Model this scenario with a cosine function, if the valve started at the top of the rotation.
What is
y=13cos(pix)+15