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

2. Stretches of Trig Functions "Certain images and/or photos on this presentation are the copyrighted property of JupiterImages and are being used with permission under license. These images and/or photos may not be copied or downloaded without permission from JupiterImages" Module C2

3. Stretches of Algebraic Functions In an earlier section, we met stretches. 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 Reminder:  ( multiplied by k )

4. Stretches of Algebraic Functions 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. ( x multiplied by k )

5. Stretches of Trig Functions e.g. 1 Sketch the graph of the function is a stretch of s.f. 2, parallel to the y -axis. Solution: We can use the fact that is a stretch of. xysin2 

6. Stretches of Trig Functions e.g. 1 Sketch the graph of the function Solution: We can use the fact that is a stretch of. xysin2  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. Stretches of Trig Functions e.g. 2 Sketch the graph of the function Solution: is a stretch of s.f., parallel to the x -axis. So,

8. Stretches of Trig Functions 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.

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

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

11. Stretches of Trig Functions Solution: 3.Sketch the graph of for showing the scales clearly. What is the period of the function? The period is Exercises

12. Stretches of Trig Functions

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. Stretches of Trig Functions 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. Stretches of Trig Functions e.g. 1 Sketch the graph of the function Solution: We can use the fact that is a stretch of. xysin2  A useful application of stretches occurs with the trigonometric functions is a stretch of s.f. 2, parallel to the y -axis.

16. Stretches of Trig Functions 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.