Graphs of the Sine and Cosine Functions

1
Graphs of the Sine and Cosine Functions

• Section 4.5

2
Objectives

• Determine the amplitude, period, and phase shift
  of the graph of a sine or cosine function given
  an equation.
• Match a graph to its equation.
• Determine the amplitude, period, and phase shift
  of the graph of a sine or cosine function given a
  graph.
• Write the equation of the graph of a sine or
  cosine function given a written description or a
  graph.

3
Vocabulary

• period
• amplitude
• midline
• phase shift
• periodic graph
• sinusoidal graph

4
Graph the function sin(x) on the interval ?2p,
2p
5
Graph the function cos(x) on the interval ?2p,
2p
6
General Function
7
Graph the function sin(x) on the interval ?2p,
2p
What is the period?  What is the midline?  What
is the amplitude?  What is the phase shift?
8
Graph the function cos(x) on the interval ?2p,
2p
What is the period?  What is the midline?  What
is the amplitude?  What is the phase shift?
9
What is the amplitude of the graph of f(x) 10
sin(x)
10
What is the period of the graph of f(x) 10
cos(6x)
11
For the graph of
What is the period?  What is the midline?  What
is the amplitude?  What is the phase shift?
12
The curve below is the graph of a sinusoidal
function.  It goes through the point (5, 2). 
Find a sinusoidal function that matches the given
graph.