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

*******