Cambridge International Mathematics

7

a y= sinx b y= sinx+2 c y= sin(x+90o) d y= cosx

What do you notice?

8

a y= cosx b y= cosx¡ 2 c y= cos(x¡ 90 o) d y= sinx

What do you notice?

Discovery The families y=asin(bx) and y=acos(bx)

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What to do:

1

a y= sinx b y= 2 sinx c y=^12 sinx

d y=¡sinx e y=¡^13 sinx f y=¡^32 sinx

2 All of the graphs in 1 have the form y=asinx:

Comment on the significance of:

a the sign ofa b the size ofa, which is jaj:

3 Use the graphing package to graph on the same set of axes:

a y= sinx b y= sin 2x c y= sin

¡ 1

2 x

¢

d y= sin 3x

4 All of the graphs in 3 have the form y= sin(bx) where b> 0.

a Doesbaffect the: i amplitude ii period?

b What is the period of y= sin(bx), b> 0?

5 Repeat 1 to 4 above, replacingsinbycos.

You should have observed that for y=asin(bx) and y=acos(bx):

² aaffects theamplitudeof the graph. It provides a stretch with invariantx-axis and scale factora.

² baffects theperiodof the graph. It provides a stretch with invarianty-axis and scale factorb.

² the amplitude isjajand the period is

360 o

b

.

GRAPHS OF y = asin(bx) AND

y =acos(bx) [3.2, 3.3, 8.8]

H

GRAPHING

PACKAGE

In this discovery we consider different transformations of the basic sine and cosine

functions.

Plot on the same set of axes for 06 x 6360 o:

Plot on the same set of axes for 06 x 6360 o:

Further trigonometry (Chapter 29) 599

Use the graphing package or a graphics calculator to graph on the same set of axes:

IGCSE01

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Y:\HAESE\IGCSE01\IG01_29\599IGCSE01_29.CDR Tuesday, 18 November 2008 11:09:55 AM PETER