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: Amplitude & Period

Overview

Altering a trigonometric function by multiplying it by a constant changes its graph by stretching it taller or squishing it flatter. This is called a change in amplitude. Altering it by multiplying its angle by a constant changes its graph by stretching / squishing it like a spring. This is called a change in period. In this lesson we learn the effect of these changes on the six trig functions.

Objectives

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

• 4.2.1 Given a trig function or graph of a trig function find its amplitude including knowing that amplitude is always positive
• 4.2.2 Know that a negative coefficient of a trig function means a reflection in the x-axis (i.e., flips the curve upside down)
• 4.2.3 Given a trig function or graph of a trig function find its period including using the formula (period of basic trig fn)/B

Terminology

Terms you should be able to define: amplitude, period (of a trig function), periodic

Text Notes

You may SKIP any "curve fitting" and "regression" examples/problems in this section and throughout the course including "sine regression".

Mini-Lectures and Examples

Supplementary Resources (recommended)

Explore how changing the "a" (amplitude) and "b" (period) values on the slider bar affect the sine graph at Sine Amplitude and Period from Desmos.

Supplemental Resources (optional)

rev. 2020-10-19