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


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.


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


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

Mini-Lectures and Examples

STUDY: Graphs - Vert. Translation, Phase Shift, Graph <-> Equation, Combinations

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