“Teach A Level Maths” Vol. 1: AS Core Modules

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Presentation transcript:

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

Module C2 "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"

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

( 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.

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.

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.

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

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.

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

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.

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

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.

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.

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.

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.