4 ¼
¼ 2 ¼ 3 ¼
Trigonometric functions (Chapter 9) 233
Example 1 Self Tutor
Without using technology, sketch the following graphs for 06 x 64 ¼:
a y= 2 sinx b y= sin 2x c y= sinx¡ 1
a The amplitude is 2 and the period is 2 ¼.
b The period is^22 ¼=¼.
) the maximum values are¼units apart.
c This is a vertical translation of y= sinx downwards by 1 unit.
The principal axis is now y=¡ 1.
EXERCISE 9B
1 Without using technology, sketch the following graphs for 06 x 64 ¼:
a y= 3 sinx b y= 4 sinx c y= sin 3x
d y= sin 4x e y= sinx+2 f y= sinx¡ 3
Check your answers using technology.
2 Find the value ofagiven that the function y=asinx, a> 0 , has amplitude:
a 2 b 5 c 11
3 Find the value ofbgiven that the function y= sinbx, b> 0 , has period:
a^23 ¼ b^25 ¼ c ¼ 3 d ¼ 2
Since has half the
period of , the first
maximum is at not.
sin 2
sin
x
x
_rpp_w
GRAPHING
PACKAGE
y
y=2y=2sinsinxx
2
-2
x
y=y=sinsinxx
O wwp_p_ pp sE_s__Epp_ 22 pp s_TT_s_pp_ 33 pp UsU_s__pp_ 44 pp
1
-1
x
y y=y=sinsinxx y=y=sinsin2x2x
O wwp_p_ pp sE_s__Epp_ 22 pp s_TT_s_pp_ 33 pp UsU_s__pp_ 44 pp
1
-1
-2
-1 y=¡¡¡¡sinx
y=¡¡¡¡¡¡sin 1x-
x
y
O _wpwp_ p EE_s__s_pp 22 pp T_s_s_Tpp_ 33 pp _sU_s_Upp_ 44 pp
-1
-1
-1
4037 Cambridge
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Y:\HAESE\CAM4037\CamAdd_09\233CamAdd_09.cdr Monday, 14 April 2014 5:59:38 PM BRIAN