Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

Course: Trigonometry
Topic: Graphs of Trigonometric Functions
Subtopic: General Equation & Graph to Equation

Overview

In this lesson we pull together all the pieces 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 where "trig" is one of the 6 trigonometric functions. 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 equation that when graphed produces a given graph of a trigonometric function

Terminology

Terms you should be able to define: general equation (form) of a trig function

Mini-Lectures and Examples

Supplemental Resources (optional)

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

rev. 2020-10-19