GTF - Graphing Trigonometric Functions Module Overview

Introduction

In this module, we will explore graphing trigonometric functions. We will take the ratios we've learned on the Unit Circle, and use those to model the graphs of sine, cosine and tangent. Finally, you will learn how to utilize those sinusoidal functions to model real world phenomena like the tides or the temperature!

Essential Questions

• What does the Unit Circle have to do with Trigonometric Functions?
• How are the amplitude, midline, period, and phase shift of a trigonometric function related to the transformation of the parent graph?
• If I know the characteristics of the graphs of a sinusoidal function, how can I write an equation of that graph?
• How can we model a real-world situation with a trigonometric function?

Graphing Trigonometric Functions Key Terms

The following key terms will help you understand the content in this module.

Sinusoidal Function - a function is considered sinusoidal if its graph has a shape of $y=\sin x$or a transformation of $y=\sin x$.

Midline - a horizontal line located halfway between the maximum and minimum values.

Amplitude - the distance from the midline to either the maximum or minimum value; ½ the distance between the maximum and minimum values.

Period - the horizontal length of one complete cycle; the distance between any two repeating points on the function.

Frequency - the number of cycles the function completes in a given interval; the reciprocal of the period.

Asymptote - a line that continually approaches a given curve but does not meet it at any finite distance.

Phase Shift - a change in the phase of a waveform.

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