Cambridge Additional Mathematics

04 ¼

BTd_p

AWd_p

OO

(0 1),

(1 0),

(0 -1),

(-1 0),

&-[[, * &[[, *

&--[[, * &[[,- *

O

() 01 ,¡

() 10 ,¡

( -1) 0 ,

(-1 ),¡ 0

&Qw]_, *

&],Qw*

&],-Qw*

&-w]Q_-, * &Qw]_-, *

&-],-Qw*

&-],Qw*

&-Qw]_, *

O

Qw

¼ 0

Th_p _yp

244 Trigonometric functions (Chapter 9)

Reminder:

Example 6 Self Tutor

Solve forx: 2 sinx¡1=0, 06 x 6 ¼

2 sinx¡1=0

) sinx=^12

There are two points on the unit circle with sine^12.

They correspond to angles¼ 6 and^56 ¼.

These are the only solutions on the domain 06 x 6 ¼,so

x=¼ 6 or^56 ¼.

Since the tangent function is periodic with period¼we see that tan(x+¼) = tanx for all values ofx.

This means that equaltanvalues are¼units apart.

Example 7 Self Tutor

Solve tanx+

p

3=0 for 0 <x< 4 ¼.

tanx+

p

3=0

) tanx=¡

p

3

There are two points on the unit

circle with tangent¡

p

3.

They correspond to angles^23 ¼ and^53 ¼.

For the domain 0 <x< 4 ¼ we have

4 solutions: x=^23 ¼,^53 ¼,^83 ¼,or^113 ¼.

EXERCISE 9E.2

1 Solve forxon the domain 06 x 64 ¼:

a 2 cosx¡1=0 b

p

2 sinx=1 c tanx=1

2 Solve forxon the domain ¡ 2 ¼ 6 x 62 ¼:

a 2 sinx¡

p

3=0 b

p

2 cosx+1=0 c tanx=¡ 1

Start at angle and work

around to , noting down

the angle every time you

reach points A and B.

0

4 ¼

(moved over +100mm to the right!)

cyan magenta yellow black

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_09\244CamAdd_09.cdr Tuesday, 28 January 2014 9:42:21 AM BRIAN