Cambridge Additional Mathematics

-4¼ - 2 ¼

2 ¼ 4 ¼ x

6

4

2

y

O

x

y

-4-4¼¼ -2-2¼¼ O 22 ¼¼ 44 ¼¼

5 ¼

Qw^3

¼

3

O

¼

O

Trigonometric functions (Chapter 9) 251

b 2 cos^2 x+ cosx¡1=0

) (2 cosx¡1)(cosx+1)=0

) cosx=^12 or¡ 1

cosx=^12 when

x=¼ 3 or^53 ¼

cosx=¡ 1 when

x=¼

The solutions are: x=¼ 3 ,¼,or^53 ¼.

EXERCISE 9G

1 Solve for 06 x 62 ¼:

a 2 sin^2 x+ sinx=0 b 2 cos^2 x= cosx c 2 cos^2 x+ cosx¡1=0

d 2 sin^2 x+ 3 sinx+1=0 e sin^2 x=2¡cosx f cosx+ secx=2

2 Solve for 06 x 62 ¼:

a sin^2 x+ cosx=¡ 1 b 2 cos^2 x= 3 sinx

Review set 9A

#endboxedheading

1 Which of the following graphs

ab

2 Draw each of the following graphs for 06 x 62 ¼:

a y= 5 sinx b y= cos 3x¡ 1 c y= tan 2x+4

3 State the minimum and maximum values of:

a 1 + sinx b 2 cos 3x c y= 3 sin 2x d y= cos 4x¡ 1

4 State the period of:

a y= 4 sinx b y= 2 cos 4x c y= 4 cos 2x+4 d y= 2 tan 3x

5 Complete the table: Function Period Amplitude Domain Range

y= 3 sin 2x+1

y= tan 2x

y= 2 cos 3x¡ 3

displays periodic behaviour?

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_09\251CamAdd_09.cdr Tuesday, 8 April 2014 10:31:19 AM BRIAN