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S = contains supplemental resources
Course: Trigonometry
Topic: Graphs of Trigonometric Functions
Subtopic: General Equation & Graph to Equation

Overview

In this lesson we pull together all the peices of a trigonometric graph into one equation called the general equation of a trigonometric function. The general equation f(x) = A trig(B(x-C)) + D gives the amplitude, period, phase shift, and vertical equation. We study going from this form of the equation to the graph, and from the graph be able to form this equation.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 4.4.1 Find amplitude, period, phase shift, and vertical translation from the general form of a trigonometric function
• 4.4.2 Find amplitude, period, phase shift, and vertical translation from a trigonometric graph
• 4.4.3 Find an equaiton that when graphed produces a given graph of a trigonometric function

Terminology

Define: general equation (form) of a trig function

Supplemental Resources (optional)

Videos from James Sousa's MathIsPower4U:
Animation:  Transformations of Sine in the form y = Asin(B(x – D)) + C
Mini-Lesson: Determining the Equations of Sine and Cosine Functions
Example: Determine the Equation of a Transformed Sine Function From a Graph