Transcript Page 309 – Amplitude, Period and Phase Shift

Page 309 – Amplitude, Period and
Phase Shift
Objective
•To find the amplitude, period and phase
shift for a trigonometric function
•To write equations of trigonometric
functions given the amplitude, period,
and phase shift
Glossary
• Amplitude
• Period
• Phase Shift
Amplitude of Sine and Cosine
Functions
The amplitude of the functions
y = A sin Q and y = A cos Q is the absolute
value of A
The tangent, cotangent, secant and cosecant functions
do not have amplitudes because their values increase
and decrease without bound.
State the amplitude of the function
y = 3 cos Q. Graph y = 3 cos Q y = cos Q on
the same set of axes. Compare the
graphs.
According to the definition of amplitude, A = 3.
Make a table of values.
Q
0°
45°
90°
cosQ
1
.71
0
3cosQ
3
2.12
0
135° 180° 225°
-.71
-2.12
270° 315° 360°
-1
-.71
0
.71
1
-3
-2.12
0
2.12
3
Graph the points and draw a smooth curve.
Period
• The period of a function is the distance on
the x-axis it takes a function to go through
one complete cycle.
The period of the functions y = sin kQ and y = cos kQ
is:
360°
k
The period of the function y = tan kQ is: 180°
k
State the period of the function
y = sin 4Q. Then graph the function and
y = sin Q on the same set of axes.
By definition, the period of the sin function is 360°/k.
Period = 360°/4 = 90°
This means the function y = sin 4Q goes through one
complete cycle in 90°.
Phase Shift
• Phase shift moves the graph of the
function horizontally.
The phase shift of the function y = A sin (kQ + c)
is: - c
k
If c > 0 the shift is to the left. If c < 0 the shift is to
the right.
This applies to all the trigonometric functions.
State the phase shift of the function
y = tan (q – 45). Then graph the
function and y = tan q on the same axes
and compare.
The phase shift is – c/k.
- - 45 = 45°
1
Since c is less than 0 the shift is to the right.
Assignment
• Page 315
– # 4 – 11, 15 - 24