Algebra II
Activity:
Getting Triggy With It
Posted on Apr 17, 2008
Topic: Trigonometric Functions & Equations
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.
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Activity Key Steps:
They will explore a general trigonometric function. Students will review definitions that will help them determine values such as maximum, minimum, and zeros geometrically.
In problem 2, students will investigate the effect of the coefficients a, b, c, and d. Where a is the amplitude, b is frequency, c is the phase shift, and d is the vertical offset.
They will use the manual data capture of the values: a, b, c, d, zero1, zero2, maximum, and minimum.
This will help students with identifying what aspect of the graph change when changing each coefficient.
In problem 3, students will take a closer look at graph features. They will set up the graph to capture values of the amplitude, period, and frequency.
They construct a segment from the first peak of the graph to the x-axis and find the distance between the two points. They will then display and calculate the frequency.
At the end of this activity, students will be able to identify the relationship between a, b, c, and d and the amplitude, frequency, and period. They will also know how to use their handheld to approximate the zeros, minima, and period of the primary trigonometric functions by graphing.