10. 90 180 270 360
1
0
-1
Y = sin x
540450
Period of graph is 3600
Cycle starts again
Also applies to Y = cos x
Between 00
and 3600
there is 1 cycle
Taking it Further
11. 90 180 270 360
1
0
-1
Y = sin 2x
Period of graph is 1800
There are 2 cycles between 00
and 3600
12. Combining these rules
Draw y = 6sin2x
Max 6
Min -6
2 cycles
Period = 360 ÷ 2 = 1800
90 180 270 360
6
0
-6
Y = 6sin 2x
15. Changing the Scale
Nice for Drawing Graphs
y = 4 Sin 6x
Cycles?
Period
6
360 ÷ 6 = 600
15 30 45 60
4
0
-4
16. 300 600
900
1200
7
Not so nice for recognising graphs
Period = 1200
No of Cycles in 360? 360 ÷ 120 = 3
y = 7 cos 3x
2400 3600
17. Find equation of graph below.
Cycles
Max 7
Negative sin
360 ÷ 60 = 6
15 30 45 60
7
0
-7
y = -7sin6x
18. Remember rules for y = (x – 3 )2
+ 5
Same rules for trig graphs!
3 units to right Up 5
Extra Trig Graph Rules
19. 90 180 270 360
4
0
-4
Y = 4cos (x – 450
)
450
Y = 4cosx 450
to right
Sketch Normal Graph
Move each point
right/left
y =4cos(x – 450
)
20. 90 180 270 360
11
0
-11
Recognising
Sin Graph
300
to right
y = 11 sin(x – 300
)
300
21. 90 180 270 360
13
0
-13
Recognising
Cos Graph
200
to left
y = 13 cos(x + 200
)
-200
22. 90 180 270 360
11
0
-11
A Bit of Confusion
Sin Graph
300
to left
y = 11 sin(x + 300
)
-300
600
Cos Graph
600
to right
y = 11 cos(x – 600
)
Both correct
23. 6
-6
y = 6cos(x + 300
)
-300
Identify this graph
900
1800
2700
3600
24. 90 180 270 360
1
0
-1
Y = sinx + 2
Y = sinx
2
3
25. 90 180 270 360
4
0
-4
Y = 4cosx + 6
8
12
range = 8
Graph Type
y = 4cosx
2
6
10
-2
Equation?
26. 90 180 270 360
0
No Maximum (or minimum)
What about y = Tanx ???
Goes to infinity
Cycle complete
Period is 1800
27. 90 180 270 360
0
Changing the period
Cycle complete
Normal Period is 1800
2 cycles
y = tan2x