3.3: Getting Triggy With It
This activity is intended to supplement Trigonometry, Chapter 2, Lesson 6.
ID: 9774
Time required: 45 minutes
Activity Overview
Students systematically explore the effect of the coefficients on the graph of sine or cosine functions. Terminology describing the graph—amplitude, period, frequency, phase shift, baseline, and vertical offset—is introduced, then reinforced as the student calculates these values directly from the graph using the graphing calculator.
Topic: Trigonometric Functions & Equations
 Approximate the zeros, minima and period of the primary trigonometric functions by graphing.
 Approximate the amplitude, frequency, and phase shift of the primary trigonometric functions by graphing.
 Given the equation of a primary trig function, state its range, amplitude, frequency, period and phase shift.

Describe how the graph of a trigonometric function \begin{align*}y = f(x)\end{align*}
y=f(x) changes under transformations.
Teacher Preparation and Notes
 Students should already have been introduced to the basic sine and cosine graphs.
Associated Materials
 Student Worksheet: Getting Triggy with It http://www.ck12.org/flexr/chapter/9700, scroll down to the third activity.
Problem 1 – A general trigonometric function
Students should start by opening the Transformation Graphing app by pressing APPS and choosing Transfrm from the list. (Hint: Press ALPHA 4 to jump to the Ts.)
In \begin{align*}Y_1\end{align*}
The Transformation Graphing app will allow students to change the values of \begin{align*}A, B, C,\end{align*}
Students can use the zero, minimum, and maximum commands (\begin{align*}2^{nd}\end{align*}
Problem 2 – The effect of the coefficients A, B, C, and D
By changing the coefficients systematically, students can figure out which coefficients affect which graph features. Students will examine each of the coefficients individually to see the effects of each on the graph of the function.
The value of \begin{align*}A\end{align*}
The value of \begin{align*}B\end{align*}
The value of \begin{align*}C\end{align*}
The phase shift of a sine function is the horizontal distance from the \begin{align*}y\end{align*}
The value of \begin{align*}D\end{align*}
Problem 3 – A closer look at amplitude, period, and frequency
Next, students will enter the general cosine function shown in \begin{align*}Y_1\end{align*}