14.1 reteaching

Name Date Class
LESSON
14-1
Reteach
Graphs of Sine and Cosine (continued)
A phase shift is a horizontal translation. Sine and cosine can be translated horizontally
by y sin x h and y cos x h .
A phase shift or horizontal translation of h units moves the graph left h units for h 0 or
right h units for h 0.
Use the graph of f x cosx to sketch the graph of g x cos x __
2 .
Step 1 Compare g x cos x __
2 to y a cosbx.
Find the amplitude and period.
The amplitude and
a 1 and F1F 1, so the amplitude is 1.
period of g are the
b 1, and ___ 2
FbF ___ 2
same as for y cosx.
2, so the period is 2.
F1F
Step 2 Find h to identify the phase shift.
x h x __ Because h 0, the shift is to the right.
__
, so h
2 2 .
The phase shift is __ radians to the right.
Intercepts occur
2
at integer
Step 3 Identify the first two positive x-intercepts.
The x-intercepts of f x cosx occur at __ and
3
2 ___
2 .
multiples of .
The x-intercepts of g x occur at __
3
, or , and ___ , or 2.
2 __ 2
Step 4 Identify the maximum and minimum values.
The maxima and minima of f x cosx occur
at 0 and .
The maxima and minima of g x occur at
3
, or ___
2 .
0 __ 2 , or __ 2 , and __ 2
Step 5 Graph f x cosx and g x cos x __
2 .
2 __ 2
Use the graph of f x sinx to sketch the graph of g x sin x __
2 .
6. Identify h. What is the phase shift?
h __ 2 ; phase shift: __ radians to the right
2
7. Identify the x-intercepts from 0 to 2.
__
2 , ___ 3
2
8. Identify the maxima and minima from 0 to 2.
Maximum of 1 at ; minimum of –1 at 0 and 2
9. Sketch the graphs of f x and g x .
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7 Holt Algebra 2
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