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GDC Set up
Ensure that your calculator is in degree mode and that you know how to adjust the v-window of your graphs before doing these trigonometry graphs.
Amplitude of sine graphs
In the graph menu on your GDC set a window using:
0 x 360 and - 3 y 3, and draw y sin x.
On the same graph draw y 2sin x. What happens?
On the same graph draw y asin x. Choose your a.
You may need to adjust your y window.
In the graph menu on your GDC set a window using:
0 x 360 and - 3 y 3, and draw y cos x.
On the same graph draw y 2sin x. What happens?
On the same graph draw y asin x. Choose your a.
You may need to adjust your y window.
Amplitude of cosine graphs
Amplitude of a trig graph
A graph of y=sin(x) is shown below.
This graph has an amplitude of 1.
The graph of y=2sin(x) has an amplitude of 2.
The graph of y=3sin(x) has an amplitude of 3.
This pattern will also work with cosine graphs.
Amplitude of trig. graphsYou will have discovered from previous slides that multiplying a trig graph by a number stretches the graph.The multiplying factor of the graph is known as the graph’s amplitude.
1. y sin x
2. y 3sin x
3. y 5cos x
4. y
1
2cos x
5. y 10sin x
Amplitude=1
Amplitude=3
Amplitude=5
Amplitude= 1
2
Amplitude=10
Amplitude of trig graphs 1
Find the amplitude of the graph below.
Amplitude=5
Find the value of a in f(x)=asinx, graphed below.
Amplitude of trig graphs 2
a 4
f (x) asin x
Period of sine graphs
In the graph menu on your GDC set a window using:
0 x 360 and -2 y 2, and draw y sin x.
On the same graph draw y sin2x. What happens?
On the same graph draw y sinbx. Choose your b.
You may need to adjust your x window.
Period of cosine graphs
In the graph menu on your GDC set a window using:
0 x 360 and -2 y 2, and draw y cos x.
On the same graph draw y cos2x. What happens?
On the same graph draw y cos bx. Choose your b.
You may need to adjust your x window.
Period of a trig graphA graph of y=cos(x) is shown below.
This graph has an period of 360 - the length it takes to make a complete wave.
The graph of y=cos(2x) has an period of 180.The graph of y=cos(3x) has an period of 120.
Period of trig. graphs
You will have discovered from previous slides that multiplying the x by a constant increases the number of ‘waves’ the graph does. This is called the period - the time it takes to complete one cycle.
y sin x takes 3600 to complete one cycle. 3600 is the period.
y sin2x takes 1800 to complete one cycle. 1800 is the period.
In general: y sinbx, the period is
360
b.
or, y cos bx, the period is
360
b.
Period of trig. graphs
Find the period of each of these graphs.
1. y sin3x
2. y sin5x
3. y cos2x
4. y cos x
5. y sin
1
2x
Period=120
Period=72
Period=180
Period=360
Period=720
Period of trig graphs 1
Find the period of the graph below.
Period=90
Vertical shift of trig. graphs
In the graph menu on your GDC set a window using:
0 x 360 and - 5 y 5, and draw y sin x.
On the same graph draw y sin x 3 What happens?
On the same graph draw y sin x c Choose your c.
You may need to adjust your y window.
Vertical shift of trig. graphs
In the graph menu on your GDC set a window using:
0 x 360 and - 5 y 5, and draw y cos x.
On the same graph draw y cos x 3 What happens?
On the same graph draw y cos x c Choose your c.
You may need to adjust your y window.
Shift of a trig graph
A graph of y=cos(x) is shown below.
Look at where this graph starts (0,1).
The graph of y=cos(x)+2 has a shift of 2.
The graph of y=cos(x)-3 has a shift of -3
This pattern will also work with sine graphs.
Vertical shift of trig. graphs
You will have discovered from previous slides that adding a constant onto the trig graph will move the graph up, or down if the constant is negative.Write down the y-coordinate where the graph crosses the y-axis for each of these functions.
1. y sin x 5
2. y sin x 7
3. y cos x 4
4. y cos x
1
2
5. y cos x 6
y 5
y 7
y 5
y
1
2
y 5
Putting it all together
y asinbx c
This is the general expression for a trig. graph which has been transformed. If you are trying to find the values of the letters then find a first, b second and c last. This format also works for cosine and tangent graphs.
AmplitudeCalculates the
period
Vertical shift
Finding a, b and c
A graph is drawn below of the function f (x) asinbx c.
Find the values of a, b and c.
a 3
b 2
c 4
6 units 2 cycles
Finding a, b and c
A graph is drawn below of the function g(x) acos bx c.
Find the values of a, b and c.
a 4
b 3
c 2
8 units
3 cycles
Finding a, b and c
A graph is drawn below of the function f (x) asinbx c.
Find the values of a, b and c.
a 4 b
1
2 c 1
Finding a, b and c
A graph is drawn below of the function g(x) acos bx c.
Find the values of a, b and c.
a
1
2 b 4 c 3
