3.3: Getting Triggy With It
This activity is intended to supplement Trigonometry, Chapter 2, Lesson 6.
Problem 1 – A general trigonometric function
Using the Transformation Graphing app, press
Complete the table.




zero1  zero2  min  max 

1  1  0  0  
4 

3  1 
Problem 2 – The effect of the coefficients A, B, C, and D
Examining A
 Set
B=1 andC=D=0 and change the value ofA . Try 4 different values ofA .




zero1  zero2  min  max 

1  0  0  
1  0  0  
1  0  0  
1  0  0 
 How did the appearance of the graph change?
 Which graph features changed? Which did not change?
 Write equations to describe the relationship between
A and the features that did change.  When
B=1 andC=D=0 , ___________________.
The value of
 Calculate the amplitude from the minimum and maximum values in the table above.
 Compare the results to the values of
A . What do you notice?
Examining B




zero1  zero2  min  max 

1  0  0  
1  0  0  
1  0  0  
1  0  0 
 Try 4 different values of
B . How did the appearance of the graph change?  Which graph features changed? Which did not change?
 Describe the relationship between
B and the features that did change.
Examining C




zero1  zero2  min  max 

1  1  0  
1  1  0  
1  1  0  
1  1  0 
 Try 4 different values of
C . How did the appearance of the graph change?  Which graph features changed? Which did not change?
 What is the effect of an increasing sequence of values for
C on the graph?  What is the effect of a decreasing sequence of values for
C on the graph?
Examining D




zero1  zero2  min  max 

1  1  0  
1  1  0  
1  1  0  
1  1  0 
 Try 4 different values of
D . How did the appearance of the graph change?  Try an increasing sequence of values for
D such as 0, 1, 2, 3, 4 ... What is the effect on the graph?  Try a decreasing sequence of values for
D such as 0, 1, 2, 3, 4 ... What is the effect on the graph?  Describe the effect of the value of
D on the graph. How does changingD change the graph features?
Problem 3 – A closer look at amplitude, period, and frequency
In
amplitude: half of the vertical distance from minimum value to maximum value
period: horizontal distance from one peak (maximum point) to the next
frequency: number of cycles per
 Write a formula to find the frequency
f given the periodp .  Use the formula to complete the table on the next page.


\begin{align*}C\end{align*}  \begin{align*}D\end{align*}  max point  min point  next max point  amplitude  period  frequency 

1  1  0  0  (0, 1)  (3.14, 1)  (6.28, 1) 
\begin{align*}\frac{1}{2}*(1  (1))\end{align*} 2 
\begin{align*}6.28  0\end{align*} 6.28 \begin{align*}2\pi\end{align*} 

1  0  0  
1  0  0  
1  0  0  
1  0  0  
1  1  0  
1  1  0  
1  1  0  
1  1  0  
1  1  0 
 Based on the results in the table, determine and record each relationship:
 \begin{align*}A\end{align*} and the amplitude
 \begin{align*}B\end{align*} and the frequency
 \begin{align*}B\end{align*} and the period
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