1. Unit #6: Graphs and Inverses of Trig Functions
Accel Precalc
Unit #6: Graphs and Inverses of Trig Functions
Lesson 9: Modeling Real World Data & Simple Harmonic Motion
EQ 1: How can you create trig models to represent real world data?

2. Modeling Data Using Trig Functions:

3. Objective: Create a model in the form
Define the variables in the model:
A =
B =
t =
h =
k =
amplitude
new period
time
phase shift
vertical shift

4. WHY?? What VIEWING WINDOW could you use?
The table below lists the normal average high temperatures for Charlotte, NC.
Month
Temp °F
January 1
51.3
July 7
90.1
February 2
55.9
August 8
88.4
March 3
64.1
September 9
82.3
April 4
72.8
October 10
72.6
May 5
79.7
November 11
62.8
June 6 86
December 12 54
Use your graphing calculator to create a scatterplot of the data.
What VIEWING WINDOW could you use?
WHY??

5. Unlike the Sinusoids, the horizontal axis of symmetry IS NOT the x-axis!!
2. a) What is the period of the function? _________
12 months
b) Find B (in  radians) . ________
3. a) What are the minimum and maximum
temperatures?
Min = _______ Max = _______
51.3
90.1
19.4
Use these values to find the amplitude. A = _______
How can you use the amplitude and the max or min to find the
horizontal axis of symmetry? k = _______
70.7

6. Place the value for k in Y1 and graph the horizontal axis of symmetry through your data set. Trace along this line to estimate the closest zero. This value represents the horizontal shift. What is an estimated value for h for this periodic function?
h = ____________

7. 5. Put your values for A, B, h, and k into the model equation
Put your values for A, B, h, and k into the model equation. Graph this with your data by placing your model equation in Y2. How well does it seem to fit?
Model for Normal High Temperature in Charlotte, NC:
y = ________________________

8. Practice Problems: Modeling Data
Work on Inverse Trig Worksheets

9. Day 61 Agenda:
DG minutes
Complete Lesson U6 L9

10. Part II: Simple Harmonic Motion

11. Equilibrium --- object is at rest; zero point
Simple Harmonic Motion Models:
RECALL:
Equilibrium --- object is at rest; zero point
|A| = amplitude Maximum displacement
from point of equilibrium

12. To find c, we must use a given point (t, cos(t)) and solve.
Ex. 1 A buoy marking a channel in the harbor bobs up and
down as the waves move past. Suppose the buoy moves a
total of 6 feet from its high point to its low point and
returns to its high point every 10 seconds. Assuming that
at t = 0 the buoy is at its high point and the middle height
of the buoy’s path is d = 0, write an equation to describe
its motion.
Should the equation be in terms of sine or cosine?
Cosine
Buoy starts here.
A = 3 10
NP = _____
To find c, we must use a given point
(t, cos(t)) and solve.
Use (0,3). WHY?

13. Solve for c.

14. To find c, we must use a given point (t, sin(t)) and solve.
Ex. 2 A weight on a spring bounces a maximum of 8 inches above and below its equilibrium (zero) point. The time for one complete cycle is 2 seconds. Write an equation to describe the motion of this weight, assume the weight is at equilibrium when t = 0.
Sine 2
NP = _____ 8
t = 0 8
To find c, we must use a given point (t, sin(t)) and solve.
Initial point
Use (0,0). WHY?

16. MODELING DATA & HARMONIC MOTION:
Assignment:
MODELING DATA & HARMONIC MOTION:
Practice Problems: Modeling Data
Worksheet: Harmonic Motion