Aim: What are the graphs of y = A sin x and
y = A cos x?
Do Now: 1. If y = 2sin x, fill in the table.
2. What are the coordinates of
maximum and minimum points?
x
y

6
0
0 1
HW: p.453 # 3 – 10

3

2
3 2
5
6

3 1
0
2
3
p.453 # 32
p.458 # 3,4,5
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y
3.0
2.5

M at h Com poser 1. 1. 5
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2.0
M at h Com poser 1. 1. 5
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1.5
1.0

2
11
6
5
3
3
2
4
3
7
6

1



y = 2sin x
0.5
5
6
2
3
1
2
1
3

1
6 -0.5
1
6
1
3
1
2
2
3
5
6

1
7
6
4
3
3
2
-1.0
-1.5

-2.0
-2.5
-3.0

5
3
11
6

2
x
y = 2sin x has the same basic pattern as
y = sin x. The only difference is the range (the
values of y)
The maximum and minimum are higher and
the value that causes these changes in high
and low is known as the amplitude and it tells
us how large the range will be.
In a regular sine curve graph (y = sin x) the range is
1  y  1.
When A (the amplitude) = 2, (y = 2 sin x) the range is
2  y  2.
When A = 3 (y = 3sin x) the range is 3  y  3.
Suppose A = -2. How will this affect the graph?
The graph is the image of y = 2sin x reflected in
the x-axis.
This range is still 2  y  2
which means the amplitude is still 2.
The graphs between y = 2 sin x and y = -2 sin x
are just opposite to each other.
Therefore, Amplitude = A
.
.
The rules work exactly the same for cosine
M at h Com poser 1. 1. 5
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y
3.0
2.5


2.0
M at h Com poser 1. 1. 5
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1.5

M at h Com poser 1. 1. 5
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
1.0
2
11
6
5
3
3
2

y = 2cos x
0.5
4
3
7
6
1
5
6
2
3
1
2
1
3
1
6 -0.5
1
6
1
3

1
2
2
3
5
6
1
-1.0
-1.5

-2.0
-2.5
-3.0

7
6
4
3

3
2
x
5
3
11
6
2
Graph y = 3cos x over 0  x  2
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3.0
y
2.5
2.0
1.5
1.0
0.5
2
11
6
5
3
3
2
4
3
7
6
1
5
6
2
3
1
2
1
3
1
6 -0.5
-1.0
-1.5
-2.0
-2.5
-3.0
x
1
6
1
3
1
2
2
3
5
6
1
7
6
4
3
3
2
5
3
11
6
2
Graph y = -2sin x over  2
 x  2
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3.0
y
2.5
2.0
1.5
1.0
0.5
2
11
6
5
3
3
2
4
3
7
6
1
5
6
2
3
1
2
1
3
1
6 -0.5
-1.0
-1.5
-2.0
-2.5
-3.0
x
1
6
1
3
1
2
2
3
5
6
1
7
6
4
3
3
2
5
3
11
6
2
State the amplitude for the following functions
a) y = -3sin x
b) y = 4cos x
1
c) y  sin x
3
3
d) y   cos x
2
Write the equation according to the graph:
1.
2.
y
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2
y
2
1
1
-1
x
x
1
2
1
3
2
-2
y  2 sin x
2
-1
1
2
1
3
2
2
-2
1
y   cos x
2