Learn how to sketch the graphs of sine and cosine functions, including applying various transformations such as vertical and horizontal stretches or compressions, shifts, and phase shifts. Understand the key concepts of amplitudes, periods, and range. The course covers graphing problems and equations involving sine and cosine functions, providing a comprehensive understanding of circular functions. Intended for individuals interested in mastering graphing techniques for sine and cosine functions.
How to Graph Sine and Cosine with Transformations
Overview
Syllabus
Introduction.
What are periodic functions?.
Revisiting the unit circle.
Sine and Cosine are periodic functions.
Revisiting sine and cosine values from the unit circle.
Revisiting the circular functions.
Values for y = sin x.
Values for y = cos x.
Basic points on a sine graph.
Graphing y = sin x over 1 period.
Graphing the sine wave, y = sin x.
Creating points from negative angle measures.
A few facts about the sine function.
Showing that sine is an odd function.
Obtaining the five key x-values for sine.
Graphing y = a sin x problem 1.
Graphing y = a sin x problem 2.
Graphing y = a sin x problem 3, reflection across x-axis.
Showing the range for y = a sin x.
Finding the amplitude.
Finding the period.
Considering a horizontal stretch or horizontal compression.
Graph of f(x) = a sin bx.
Graphing f(x) = 3 sin 2x.
Graphing f(x) = 3 sin x/3.
What is a phase shift?.
Graphing y = 4 sin (2x - 2Ï€/3).
Vertical shift.
Graphing y = 4 sin (3x + 3Ï€/4) - 1.
Graphing y = cos x.
Graphing y = 3 cos (3x + 2Ï€/3) + 2.
Taught by
GreeneMath.com
