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Calculus IV
15.Functions of Several Variables
16.Multiple Integration
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S = contains supplemental resources
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:

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)

Videos from James Sousa's MathIsPower4U:
Mini-Lesson: Horizontal and Vertical Translations of Sine and Cosine
Mini-Lesson: Graphing Sine and Cosine with Various Transformations
Examples:
Example:  Describe the Transformations of a Trig Function from a Graph
Example 1:  Graphing a Transformation of Sine and Cosine
Example 2:  Graphing a Transformation of Sine and Cosine
Example 3:  Graphing a Transformation of Sine and Cosine
Example 4:  Graphing a Transformation of Sine and Cosine
Example:  Graphing a Transformation of the Cotangent Function
Example:  Graphing a Transformation of Cosecant Function