1. “Teach A Level Maths” Vol. 1: AS Core Modules
44: Stretches of the Trigonometric Functions
© Christine Crisp

2. Module C2
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3. In an earlier section, we met stretches.
Reminder:
( multiplied by k )
is a stretch of scale factor ( s.f. ) k, parallel to the y-axis
e.g.
is a stretch of s.f. 2, parallel to the y-axis

4. ( x multiplied by k )
is a stretch of scale factor ( s.f. ) , parallel to the x-axis.
e.g.
is a stretch of s.f parallel to the x-axis.

5. x y sin 2 = e.g. 1 Sketch the graph of the function
Solution: We can use the fact that is a stretch of x y
sin 2 =
is a stretch of s.f. 2, parallel to the y-axis.

6. x y sin 2 = e.g. 1 Sketch the graph of the function
Solution: We can use the fact that is a stretch of x y
sin 2 =
is a stretch of s.f. 2, parallel to the y-axis.
The scale factor of the stretch gives the amplitude of the function.

7. e.g. 2 Sketch the graph of the function
Solution:
stretch of s.f. , parallel to the x-axis. So,
is a

8. e.g. 2 Sketch the graph of the function
Solution:
stretch of s.f. , parallel to the x-axis. So,
is a
The period of is or radians.

9. Exercises
1. Give the equation of the function that is shown on the sketch below.
Ans:

10. Exercises
Sketch both functions on the same axes for the interval
2. Describe in words the transformation
Solution:
A stretch of s.f. 2 parallel to the x-axis.

11. Exercises
Sketch the graph of for
showing the scales clearly. What is the period of the function?
Solution:
The period is

13. The following slides contain repeats of information on earlier slides, shown without colour, so that they can be printed and photocopied.
For most purposes the slides can be printed as “Handouts” with up to 6 slides per sheet.

14. is a stretch of scale factor ( s.f. ) k, parallel to the y-axis e.g.
is a stretch of s.f. 2, parallel to the y-axis.
is a stretch of scale factor ( s.f. ) , parallel to the x-axis e.g.
stretch of s.f. , parallel to the x-axis.
The scale factor gives the amplitude of the function.

15. e.g. 1 Sketch the graph of the function
Solution: We can use the fact that is a stretch of x y
sin 2 =
A useful application of stretches occurs with the trigonometric functions
is a stretch of s.f. 2, parallel to the y-axis.

16. e.g. 2 Sketch the graph of the function
Solution:
is a
stretch of s.f. , parallel to the x-axis. So,
The period of is or radians.