Students are to find the equations of graphs of trigonometric functions (using sine and cosine) and will also identify values for the amplitude, period, phase shift, and vertical shift.

This activity is a modified version of the activity "What's the Equation?" originally made by Lauren Jensen.

This investigation offers opportunities for review and consolidation of key concepts related to trigonometric functions. As such, care should be taken to provide ample time for ALL students to engage actively with the requirements of the task, allowing some who may have missed aspects of earlier work the opportunity to build new and deeper understanding.

At the Advanced Algebra/Pre-Calculus level, this activity can serve to consolidate earlier work on trigonometric functions. It offers a suitable introduction to exploring trigonometric graphs, model fitting using trigonometric functions, and interpretation of graphs.

Begin by reviewing with students the general trigonometric form of the cosine function f(x) = Acos(kx - c) + h where A is amplitude, 2π/k is the period, -c/k is the phase shift, and h is vertical shift. Do the same for the sine function.

The screenshots on page 2 demonstrate expected student results. Refer to the screenshots on pages 3 and 4 for a preview of the student .tns file.

View the activity file for step-by-step directions for the activity.

View the activity file for assessments/evaluations and activity extensions.