matematika - graph of cosinus function
TRANSCRIPT
Graph of Cosinus
Function Cosinus Table
x
Cos x
0˚
1
30˚ 45˚ 60˚ 90˚ 120˚ 135˚ 150˚ 180˚
0 -1
1
-1
90˚ 180˚ 270˚ 360˚ 450˚ 540˚ 630˚ 720˚
-1
90˚ 180˚ 360˚
1
270˚ 0 y=cosx
2
3
4
5
6
7
8
y=cosx+3
y=cosx+1
y=cosx+2
CONCLUSION
MAXIMUM VALUE OF COSINUS MINIMUM VALUE OF COSINUS
1 -1
A SIMPLE FORM OF TRYGONOMETRY
FUNCTION
Y = a cos kx a = amplitudo
Perioda(P)=
Example:
Determine the max value, min value, and the period from the function below!
1)y = 4 cos 3x
y max= 4 ….. = ……… (1) 4
y min= 4 ….. = ……… (-1) -4 P= = 120˚
2)y = 5cos 5 x + 5
y max= 5 ….. +5 = ………
y min= 5 ….. +5 = ………
10 0
(1)
(-1)
P= = 72˚
How about the
graph??
Example:
Determine the max value, min value, the period,coordinate, and graph from the function below!
1. y= cos (2x – 60˚) + 7 0˚≤ x ≤ 360˚
y max= ….. +7 = ………
y min= ….. +7 = ………
(1)
(-1) 6
8
P= = 360˚
Make a simple function before!
a) cos(2x – 60˚) = 0
Cos 2x – 60˚ = Cos 90˚
Who is know the value from arc cos
0?
2x – 60˚ = 90˚ + k. 360˚
2x = 90˚+ 60˚ + k.360˚
2x = 150˚ + k.360˚
x = 75˚ + k.180˚
k=0
k=1
x = 75˚
x= 255˚
(75˚,0)
(255˚,0)
b) cos(2x – 60˚) = 1
Cos 2x – 60˚ = Cos 0˚
Who is know the value from arc cos
1?
2x = 0˚+ 60˚ + k.360˚
2x = 60˚ + k.360˚
x = 30˚ + k.180˚
k=0
k=1
x = 30˚
x= 210
(30˚,1)
(210˚,1)
c) cos(2x – 60˚) = -1
Cos 2x – 60˚ = Cos 180˚
Who is know the value from arc cos
-1?
2x = 180˚+ 60˚ + k.360˚
2x = 240˚ + k.360˚
x = 120˚ + k.180˚
k=0
k=1
x = 120˚
x= 300˚
(120˚,-1)
(300˚,-1)
(255˚,0) (210 ˚,1) (300˚,-1) (75˚,0) (120˚,-1) (30˚,1)
-1
90˚ 180˚ 360˚
1
270˚ 0 30˚ 75˚ 120˚ 165˚ 210˚ 255˚ 300˚ 345˚
coordinate
y=cos2x-60˚
y=cosx
-1
75˚
1
0 30˚ 120˚ 165˚ 210˚ 255˚ 300˚ 345˚
y=cos2x-60˚
7
6
8 y=cos(2x-60˚)+7
NOTE BOOK!!!
1.From the function form y= a cos (kx+) +c we get conclusion:
Ymax = a + c Ymin = -a + c
P=
2. If alpha () is positive so the graph will move to left!
3. If alpha () is negative so the graph will move to right!
As far as
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