13-5The cosine Function
Today’s Objective:
I can graph the cosine function.
𝑦=co s 𝑥
𝑓 (𝑥 )=sin 𝑥x y
0
x
y
-3p -5p
2-2p -3p
2-p -p
2
p
2p 3p
22p 5p
23p
-2
-1
1
2
x
y
Domain:
Range:
Period:
Amplitude:
All real numbers
– 1 ≤ y ≤ 1
2π
1
𝑦=cos 𝑥 𝑦=𝑐𝑜𝑠 𝜃OR
-3p -5p
2-2p -3p
2-p -p
2
p
2p 3p
22p 5p
23p
-2
-1
1
2
x
y
How does this graph differ from y = sin x?
Translated left by
𝜋2
x
y
Properties of Cosine Function
𝑦=𝒂cos𝒃𝑥 b = # of cycles from 0 to 2πPeriod of function =
= amplitude– a = reflects graph across x-axis
Sketch the graph of:
𝑦=𝟏 .𝟓cos𝟐 𝑥 𝑦=𝟐cos𝑥𝟑
p
2p 3p
22p
-2
-1
1
2
x
y
p
2p 3p
22p
-2
-1
1
2
x
y
p
2p 3p
22p
-2
-1
1
2
x
y
p
2p 3p
22p
-2
-1
1
2
x
y
x
y
p 2p 3p 4p 5p 6p-2
-1
1
2
x
y
p 2p 3p 4p 5p 6p-2
-1
1
2
x
y
p 2p 3p 4p 5p 6p-2
-1
1
2
x
y
5 points: max – midline – min – midline - max
What is the cosine function that models the water level in inches as a function of time?
Amplitude:12
(60 )=¿30Period:
4:40 pm – 10:30 am hrs
1213=
2𝜋𝑏
𝑦=𝒂cos𝒃𝑥
𝑏=6𝜋37
𝑓 (𝑡 )=−𝟑𝟎cos𝟔𝝅𝟑𝟕
𝑥
𝑎=−30
2()=¿
My boat needs 10 inches above an average water level. When can I bring my boat into this dock?
p. 864: 7-19 odd, 27-33
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