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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

Define: translation, phase shift

Supplemental Resources (recommended)

Explore how changing the "c" and "d" values affect the graph at www.analyzemath.com/trigonometry/sine_applet.html.

Supplemental Resources (optional)