1. TRIGONOMETRIC GRAPHS

2. SINE GRAPHS The trig function “Sine” can be sketched Example 1:
a) Complete the table of y = sinx for x [0°; 360°] 0°
30°
45°
60°
90°
120°
135°
150°
180°
y = sin x
210°
225°
240°
270°
300°
315°
330°
360°
y = sin x

3. Link between sinx as a ratio and as a graph

4. b) Determine the following based on the graph:
The maximum value is…. 1
The minimum value is … -1
Amplitude
= (maximum - minimum value) divided by 2
= (1-(-1)) = =1
c) Determine:
The domain of the graph is …
The range of the graph is …

5. Example 2:
a) Draw the graph of y = sin x for x [-360°; 360°]
b) After how many degrees does the graph (pattern) start repeating itself? … 360°
This is called the period of the graph.

6. Exercise Graph Amplitude Maximum Minimum Period
y = sin x
y = 2 sin x
y =3 sin x
y = - sin x
y = - 2 sin x
The effects of a in y = asinx
Amplitude shifts of y = asinx

7. Exercise Graph Amplitude Maximum Minimum Period
y = sin x
y = sin x + 1
y = sin x - 2
Vertical shifts of y = sinx + q

8. COS GRAPHS The trig function “Cosine” can be sketched Example 1:
a) Complete the table of y = cosx for x [0°; 360°] 0°
30°
45°
60°
90°
120°
135°
150°
180°
y = cos x
210°
225°
240°
270°
300°
315°
330°
360°
y = cos x

9. Link between cosx as a ratio and as a graph

10. b) Determine the following based on the graph:
The maximum value is…. 1
The minimum value is … -1
Amplitude
= (maximum - minimum value) divided by 2
= (1-(-1)) = =1
c) Determine:
The domain of the graph is …
The range of the graph is …

11. Example a) Draw the graph of y = cosx for x [-360°; 360°]
b) After how many degrees does the graph (pattern) start repeating itself? … 360°
This is called the period of the graph.

12. Exercise Graph Amplitude Maximum Minimum Period y = cos x y= 2 cos x
y = - 2 scos x

13. Exercise Graph Amplitude Maximum Minimum Period y = cos x

14. TAN GRAPHS The trig function “Tangent” can be sketched Example 1:
a) Complete the table of y = tan x for x [0°; 360°]
x is undefined at 90◦ and 270◦
Therefore, the tan graph has ASYMPTOTES at
x = 90◦ and
x = 270◦ 0°
45°
90°
135°
180°
y = tan x
225°
270°
315°
360°
y = tan x

16. b) Determine the following based on the graph:
The maximum value is…. There is none!
The minimum value is … There is none!
Amplitude - There is none!
However: y = atanx … a is the “amplitude”
c) Determine:
The domain of the graph is …
The range of the graph is …

17. Example a) Draw the graph of y = tan x for x [-360°; 360°]
b) After how many degrees does the graph (pattern) start repeating itself? … 180°
This is called the period of the graph.

18. Exercise Graph Amplitude Maximum Minimum Period y = tan x y= 2 tan x

19. Exercise Graph Amplitude Maximum Minimum Period y = tan x