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: Combination Graphs

Overview

A combination function means combining functions together by adding, multiplying, or composing. In this lesson we graph combination trig functions and analyze them. This can be accomplished algebraically combining coordinates x by x. This is logically interesting, but I recommend using technology to produce the graphs instead so we can concentrate on analyzing the graph without the tedium of plotting it point by point. There is a lot to discover here, so have your grapher at hand!

Objectives

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

• 4.5.1 Graph combinations of trig functions electronically
• 4.5.2 Determe if a combination trig function is periodic by observation of its graph
• 4.5.3 Analyze, i.e., interpret the period, intercepts, and relative extrema, trigonometric graphs that model applications in engineering, science, etc.

Terminology

Terms you should be able to define: combination trigonometric function, relative extreme points, relative extreme values

Mini-Lectures and Examples

rev. 2020-10-19