Quiz Review: Applications of Trig Functions
The Pendulum
A yo-yo was set in motion and a CBR unit recorded both the
distance of the yo-yo from the CBR and the time in seconds.
Time(sec)
Distance (ft)
0
.25
.5
.8
.9
1
1.25
1.5
1.7
1.8
2
2.4
2.6
2.7
3
2
2.5
3
2.5
2
1.5
1
1.5
2
2.5
3
2.5
2
1.5
1
Graph a scatter plot of the data and answer the following questions.
1. Use the right arrow key to trace along the curve to the first maximum point. Record the values below as
(x1, y1). Trace to the next minimum point after the first maximum point and record this value as (x2, y2).
Trace to the next maximum point and record below as (x3, y3).
First maximum:
x1 = _________________ y1 = _________________
Minimum:
x2 = _________________ y2 = _________________
Second Maximum:
x3 = _________________ y3 = _________________
2. The distance from the maximum to the minimum is twice the amplitude. To find the amplitude, subtract
the minimum (y2) from the maximum (y3 or y1) and then divide by two. Compare this value to the distance
from the pendulum’s rest position to the point it was pulled back.
A = _________________
3.
The average between the maximum and the minimum values is the vertical shift. Find the vertical
shift by adding the maximum (y3 or y1) and minimum (y2) together and dividing by two.
D = _________________
4.
The phase shift for a cosine curve would be the time at which the first maximum occurs. Record
the time the first maximum occurs below as C.
C = _________________
5.
The difference in time between the first two maximum values is the period. Find the period by
subtracting x1 from x3. Compare the period to the average time per cycle found in Data Collection question
4.
P = _________________
6.
The general equation of the cosine curve is
y = A cos( B( x ! C )) + D where B =
2!
. Find
P
B by dividing 2 ! by the period.
B = _________________
7.
Use the values A, B, C and D found in questions 2 through 6 to write the equation for the cosine
function that would model the motion of the pendulum.
Y = _________________
Quiz Review: Applications of Trig Functions
Average Daily Temperature in Alaska
1.)
2.)
3.)
Enter you data in the lists on the graphing calculator
Create a scatterplot of the data in your graphing calculator.
Find a sinusoidal regression y = a sin (bx+c) + d equation to model your
data and record the equation below (Use your graphing calculator)
4.)
Enter your model in y = to graph it. How well does your model fit the
data?
5.)
What is the amplitude of your model ?
6.)
Approximate the period of your model.
7.)
Use your equation to predict temperature in Fairbanks Alaska on
December 1.
Geometer’s Sketchpad: Open up the Geometer’s Sketchpad sketch on my
web page to help you to answer the following questions.
1.) Move the slider so that a = 4, b = 4, c = 0 and d = 5.
a.) What is the equation of your graph?
b.) How does the parent translate to produce this new function?
c.) What is the amplitude of the function?
d.) What is the period of the function?
2.) Move the slider so that a= -2, b = .5 , c = 0 and d = -2.
a.) What is the equation of your graph?
b). How does the parent translate to produce this new function?
c.) What is the amplitude of the function?
d.) What is the period of the function?