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3.3: Getting Triggy With It

Difficulty Level: At Grade Created by: CK-12

This activity is intended to supplement Trigonometry, Chapter 2, Lesson 6.

Problem 1 – A general trigonometric function

Using the Transformation Graphing app, press Y= and enter the general sine function in Y_1,

Y_1 = A \ ^* \ \sin(B \ ^* \ X + C) + D.

Complete the table.

A B C D zero1 zero2 min max
1 1 0 0
4 \frac{1}{2} 3 1

Problem 2 – The effect of the coefficients A, B, C, and D

Examining A

  • Set B = 1 and C = D = 0 and change the value of A. Try 4 different values of A.
A B C D 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 and C = D = 0, ___________________.

The value of A 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 A. What do you notice?

Examining B

A B C D 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

A B C D 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

A B C 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 changing D change the graph features?

Problem 3 – A closer look at amplitude, period, and frequency

In Y_1, enter the general cosine function, A \ ^* \ \cos(B \ ^* \ X + C) + D.

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 2\pi interval

  • Write a formula to find the frequency f given the period p.
  • Use the formula to complete the table on the next page.
A B C D max point min point next max point amplitude period frequency
1 1 0 0 (0, 1) (3.14, -1) (6.28, 1)

\frac{1}{2}*(1 - (-1))

2

6.28 - 0

6.28

2\pi

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:
    • A and the amplitude
    • B and the frequency
    • B and the period

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Date Created:

Feb 23, 2012

Last Modified:

Nov 04, 2014
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TI.MAT.ENG.SE.1.Trigonometry.3.3

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