Cambridge Additional Mathematics

-2

2

3

1

3

-3

¼ 2 ¼ x

y

y = 3_¡¡cos2_x

O _wp E_s_p

11

y

O 2 ¼ 4 ¼ x

33

-2-2

y

O 2 ¼ x

2

Trigonometric functions (Chapter 9) 237

Example 3 Self Tutor

Without using technology, sketch the graph of y= 3 cos 2x for 06 x 62 ¼.

a=3, so the amplitude is 3.

b=2, so the period is

2 ¼

b

=

2 ¼

2

=¼.

EXERCISE 9C

1 Without using technology, sketch the following graphs for 06 x 62 ¼:

a y= 3 cosx b y= 5 cosx c y= cos 2x

d y= cos 3x e y= cosx+2 f y= cosx¡ 1

g y= 2 cos 2x h y= cos 3x+1 i y= 4 cosx+10

j y= 2 cos 3x+4 k y= 4 cos 2x¡ 2 l y= 3 cos 2x+5

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

a amplitude 4 , period^23 ¼, and principal axis y=¡ 1

b amplitude 3 , period^25 ¼, and principal axis y=3.

3 Find the cosine function shown in the graph:

ab

4 The function y=acosbx+c, a> 0 , b> 0 , has amplitude 5 , period 2 ¼, and principal axis y=1.

a Find the values ofa,b, andc. b Sketch the function for 06 x 62 ¼.

5 The graph shown has the form y=acosbx+c

where a> 0 , b> 0.

a Find the values ofa,b, andc.

b Sketch the reflection of the function in the

x-axis.

c Write down the equation of the reflection inb. -3-3

y

x

O "y "e "w Wd"

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_09\237CamAdd_09.cdr Tuesday, 28 January 2014 9:35:15 AM BRIAN