How to Graph Sine and Cosine with Transformations

This lesson explains how to sketch sine and cosine graphs using the unit circle and periodic functions. It covers amplitude, period, reflections, phase shifts, vertical shifts, and horizontal transformations through worked examples.

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 - 2π/3).
Vertical shift.
Graphing y = 4 sin (3x + 3π/4) - 1.
Graphing y = cos x.
Graphing y = 3 cos (3x + 2π/3) + 2.