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: Vertical Translations & Phase Shift

Overview

Altering a trigonometric function by adding to it a constant changes its graph by shifting it up or down. This is called a vertical translation. Altering it by adding a constant to its angle shifts it left or right. This horizontal shift is called a phase shift. 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:

• 4.3.1 Given a trig function or graph of a trig function find its vertical translation up or down
• 4.3.2 Given a trig function or graph of a trig function find its phase shift
• 4.3.3 Know how to find, based on the signs, the direction of vertical translation and the direction of phase shift
• 4.3.4 Know that if a trig expression has a coefficient on the angle, factoring the angle can help you to algebraically find the phase shift (e.g. y=cos(2x-6)=cos(2(x-3)) has a PS 3 to the right) or know how to find the PS using the formula C/B

Terminology

Terms you should be able to define: translation, phase shift

Mini-Lectures and Examples

Supplemental Resources (recommended)

Explore how changing the "c" (phase shift) and "d" (vertical translation) values on the slider bar affect the sine graph at Sine Curve Transformations via Geogebra.

Supplemental Resources (optional)

rev. 2020-10-19