Trigonometric Graphs. What is to be learned? How to draw and identify graphs with sine and cosine.
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Transcript of Trigonometric Graphs. What is to be learned? How to draw and identify graphs with sine and cosine.
Trigonometric Graphs
What is to be learned?
• How to draw and identify graphs with sine and cosine
Y = sinx
0 30 60 90 120 150 180 210 240 270 300 330 360x
Sin x 0 10.5 0.870.87 00.5 -0.5-0.5 -0.87-0.87 -1 0
30 60 90 120 150 180 210 220 270 300 330 360
1
0.5
-0.5
-1
0
90 180 270 360
1
0
-1
Y = sinx
Maximum Value = 1
Minimum Value = -1
90 180 270 360
1
0
-1
Y = cosx
Maximum Value = 1
Minimum Value = -1
90 180 270 360
7
0
-7
Y = 7sinx
Maximum Value = 7
Minimum Value = -7
90 180 270 360
4
0
-4
Y = 4cosx
Maximum Value = 4
Minimum Value = -4
90 180 270 360
8
0
-8
Y = - 8sinx
Maximum Value = 8
Minimum Value = -8
“Opposite” to Sin x
Trigonometric Graphs
• Vital to know the basic shape of sin and cos
• The same rules apply to each
90 180 270 360
1
0
-1
Y = sinx
Maximum Value = 1
Minimum Value = -1
90 180 270 360
1
0
-1
Y = cosx
Maximum Value = 1
Minimum Value = -1
90 180 270 360
11
0
-11
Type y = A Sinx
Max Value = 11Min Value = -11
If there is a number in front, the graph is the same basic shape, but the limits change
y = 11 sinx
90 180 270 360
9
0
-9
Y = -9sinx
“Opposite” to Sin x
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
90 180 270 360
1
0
-1
Y = sin 2x
Period of graph is 1800
There are 2 cycles between 00 and 3600
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
Recognising Graph
Max 8
Min -8
4 cycles
90 180 270 360
8
0
-8
Y = 8cos4x
Cosine
Type y = sin bx
Number in front of x tells how many “cycles” there are
y = Sin 3x has 3 cycles
Length of each cycle is called the period.
Period of y = sinx is 3600
Period of y = sin3x
= 360 ÷ 3 = 1200
(up to 3600)
Combining our two rules
Draw y = 8sin2x
Max 8
Min -8
2 cycles
Period = 360 ÷ 2 = 1800
90 180 270 360
8
0
-8
Y = 8sin 2x
Changing the ScaleNice for Drawing Graphs y = 6 Sin 3x
Cycles?
Period3
360 ÷ 3 = 1200
30 60 90 120
6
0
-6
150 300 450 600
8
0
-8
Not so nice for recognising graphs
Period = 600
No of Cycles? 360 ÷ 60 = 6
y = 8 cos 6x
Remember rules for y = (x – 3 )2 + 5
Same rules for trig graphs!
3 units to right Up 5
Extra Trig Graph Rules
90 180 270 360
4
0
-4
Y = 4cos (x – 450)
450
Y = 4cosx
450 to right
90 180 270 360
4
0
-4
Y = 4cos (x – 450)
450
Y = 4cosx always draw normal graph first as a guide
90 180 270 360
1
0
-1
Y = sinx + 2
Y = sinx
2
3
90 180 270 3600
No Maximum (or minimum)
What about y = Tanx ???Goes to infinity
Cycle completePeriod is 1800
