Cambridge Additional Mathematics

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