This activity is intended to supplement Trigonometry, Chapter 2, Lesson 6.
Time required: 45 minutes
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 y=f(x) changes under transformations.
Teacher Preparation and Notes
Students should already have been introduced to the basic sine and cosine graphs.
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.)
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.
Problem 3 – A closer look at amplitude, period, and frequency