Cambridge Additional Mathematics

GRAPHING

PACKAGE

¼ 2 ¼ 3 ¼

ABC

1

• 1

1 2345678910

y= 04.

x

y

¼ 2 32 ¼ 52 ¼ yx=cos¡

11

• 
  
  
  
  • 11
  
  
  
  

11 22 33 44 55 66 77 99 1010 xx

yy

yxyx==coscos¡¡

OO

y 0.4y 0.4==

E_s__sE_pp T_s_sT_p_p

¼¼

_wp_wp

22 ¼¼ 33 ¼¼

AA BB CC

88

1

• 1

12345678910

x

y

yx=cos¡

11

• 
  
  
  
  • 11
  
  
  
  

11 22 33 44 55 66 77 88 99 1010 xx

yy

yxyx==coscos¡¡

OO

Trigonometric functions (Chapter 9) 241

If a periodic function f(x) has periodpthen the domain 06 x<pis called theprincipal domain.

By solving an equation on the principal domain, all the other solutions can be found using the periodic

behaviour.

If x=a is a solution, then x=a+kp will also be a solution for all k 2 Z.

For example, sinx has period 2 ¼, so it is normal to consider the domain 06 x< 2 ¼.

Discussion

#endboxedheading

What would you choose as the principal domain for:

² y= cosx ² y= sin(2x) ² y= tanx?

GRAPHICAL SOLUTION OF TRIGONOMETRIC EQUATIONS

Sometimes simple trigonometric graphs are available on grid paper. In such cases we can estimate solutions

straight from the graph.

Example 5 Self Tutor

Solve cosx=0: 4 for 06 x 610 radians using the graph of y= cosx.

y=0: 4 meets y= cosx at A, B, and C. Hence x¼ 1 : 2 , 5 : 1 ,or 7 : 4.

The solutions of cosx=0: 4 for 06 x 610 radians are 1 : 2 , 5 : 1 , and 7 : 4.

Trigonometric equations may also be solved using the graphing package.

4037 Cambridge

cyan magenta yellow black Additional Mathematics

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\CAM4037\CamAdd_09\241CamAdd_09.cdr Monday, 23 December 2013 3:20:47 PM BRIAN