1. 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.

2. Amplitude of sine graphs

3. Amplitude of cosine graphs

4. 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.

5. Amplitude of trig. graphs
You 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.

6. Amplitude of trig graphs 1
Find the amplitude of the graph below.

7. Amplitude of trig graphs 2
Find the value of a in f(x)=asinx, graphed below.

8. Period of sine graphs

9. Period of cosine graphs

10. Period of a trig graph A 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.

11. 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.

12. Period of trig. graphs
Find the period of each of these graphs.

13. Period of trig graphs 1
Find the period of the graph below.

14. Vertical shift of trig. graphs

15. Vertical shift of trig. graphs

16. 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.

17. 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.

18. Putting it all together
Amplitude
Vertical shift
Calculates the period
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.

19. Finding a, b and c

20. Finding a, b and c

21. Finding a, b and c

22. Finding a, b and c