Graphs of Trigonometric
Functions
Translations of Sine and Cosine
Functions
Review
•
Horizontal and Vertical Transformations
of Trigonometric functions
• As we learned with other graphs such as the
parabola, we can translate a graph vertically and
horizontally. We can also expand it or compress it.
• A horizontal transformation or shift of a
trigonometric function is called a phase shift.
• The following video will investigate the properties
of a, b, c, d of the general trigonometric function.
Our book uses a, k, c, h. It does not matter what
letter you choose to represent the general
equation.
The properties
• The standard form of the trigonometric function is y
= a sin ( bx +c) +d and
y=a cos ( bx +c )+d
The a will vertically expand the graph or vertically
compress the graph (changing the amplitude and
range)
The d will move the entire graph up or down
(changing the range)
The b will horizontally expand or compress the graph
(changing the period)
The c will move the entire graph to the right or left.
HW# 47
• Section 6-5
• Pp. 383-386
• #14-24 all, 27, 29, 30, 49