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