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 and enter the general sine function in ,
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 and and change the value of . Try 4 different values of .
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 and the features that did change.
 When and , ___________________.
The value of is the amplitude. It is equal to half of the difference between its maximum and minimum values.
 Calculate the amplitude from the minimum and maximum values in the table above.
 Compare the results to the values of . 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 . How did the appearance of the graph change?
 Which graph features changed? Which did not change?
 Describe the relationship between 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 . 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 on the graph?
 What is the effect of a decreasing sequence of values for 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 . How did the appearance of the graph change?
 Try an increasing sequence of values for such as 0, 1, 2, 3, 4 ... What is the effect on the graph?
 Try a decreasing sequence of values for such as 0, 1, 2, 3, 4 ... What is the effect on the graph?
 Describe the effect of the value of on the graph. How does changing change the graph features?
Problem 3 – A closer look at amplitude, period, and frequency
In , enter the general cosine function, .
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 interval
 Write a formula to find the frequency given the period .
 Use the formula to complete the table on the next page.
max point  min point  next max point  amplitude  period  frequency  

1  1  0  0  (0, 1)  (3.14, 1)  (6.28, 1) 
2 
6.28


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:
 and the amplitude
 and the frequency
 and the period