Cambridge Additional Mathematics

232 Trigonometric functions (Chapter 9)

2 Use the software to help complete the table:

b Function Maximum Minimum Period Amplitude

1 y= sinx 1 ¡ 1 2 ¼ 1

2 y= sin 2x

3 y= sin 3x

1

2 y= sin(

1

2 x)

b y= sinbx

3 How doesbaffect the function y= sinbx?

Discovery 3 The family y= sinx+c

Click on the icon to explore the family y= sinx+c.

What to do:

1 Use the slider to vary the value ofc. Observe the changes to the graph of

the function.

2 Use the software to help complete the table:

d Function Maximum Minimum Period Amplitude

0 y= sinx 1 ¡ 1 2 ¼ 1

3 y= sinx+3

¡ 2 y= sinx¡ 2

d y= sinx+c

3 How doescaffect the function y= sinx+c?

THE GENERAL SINE FUNCTION

DYNAMIC

SINE FUNCTION

Thegeneral sine functionis

y=asinbx+c where a> 0 , b> 0.

affects

amplitude

affects

period

affects

vertical translation

Theprincipal axisof the general sine function is y=c.

Theperiodof the general sine function is

2 ¼

b

.

Theamplitudeof the general sine function isa.

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_09\232CamAdd_09.cdr Monday, 23 December 2013 2:08:46 PM BRIAN