Cambridge Additional Mathematics

y=2sin3x+1

_wp p E_s_p 2 p

234 Trigonometric functions (Chapter 9)

4 Find the value ofcgiven that the function y= sinx+c has principal axis:

a y=3 b y=¡ 1 c y=5

Example 2 Self Tutor

Without using technology, sketch y= 2 sin 3x+1

We start with y= sinx. We then:

² double the amplitude to produce y= 2 sinx, then

² divide the period by 3 to produce y= 2 sin 3x, then

² translate the graph 1 unit upwards to produce y= 2 sin 3x+1, so the principal axis is

now y=1.

5 Without using technology, sketch the following graphs

a y= 3 sinx¡ 1 b y= 2 sin 3x c y= sin 2x+3

d y= 3 sin 2x¡ 1 e y= 5 sin 2x+3 f y= 4 sin 3x¡ 2

Check your answers using technology.

6 Finda,b, andcgiven that the function y=asinbx+c, a> 0 , b> 0 , has:

a amplitude 3 , period 2 ¼, and principal axis y=0

b amplitude 2 , period^25 ¼, and principal axis y=6

c amplitude 5 , period^23 ¼, and principal axis y=¡ 2.

7 Findmandngiven the following graph of the function y=msinx+n.

8 On the same set of axes,

a y= sinx and y=jsinxj b y= 3 sin 2x and y=j3 sin 2xj

y

y=2y=2sinsin3x+13x+1

2

-1

O pp 22 pp x

3

1

y=1

_eepp_ Wd_dW_pp Rd_dRp_p Td_Tdp_p

for 06 x 62 ¼.

for 06 x 62 ¼:

sketch for 06 x 62 ¼:

-2

-4

y

x

-1

-5

O

1

-_p_w pw_ ¼ _sEp_ 2 ¼

-3-3

cyan magenta yellow black

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_09\234CamAdd_09.cdr Friday, 31 January 2014 11:32:52 AM GR8GREG