Cambridge Additional Mathematics

DEMO

GRAPHING

PACKAGE

y a bx c

x

has a maximum

when.

= cos +

=0

DYNAMIC

COSINE

FUNCTION

10

y

x

μ

O

d

y

x

y=cosx

y=sinx

O p_pw_w pp E_sE_s_pp_ 22 pp _TT_s_spp_

-__wp

-__wp -__wp

10

-10

5050 time s()

horizontal displacement m()

100100

d=10cosμ

O

236 Trigonometric functions (Chapter 9)

We return to the Ferris wheel and now view the movement of the green light from above.

Now cosμ=

d

10

so d= 10 cosμ.

The graph being generated over time is therefore acosine function.

Use the graphing package to graph y= cosx and y= sinx on the same set of axes.

Like the sine curve y= sinx, the cosine curve y= cosxhas aperiodof 2 ¼,anamplitude

of 1 , and itsrangeis ¡ 16 y 61.

You should observe that y= cosx and y= sinx

are identical in shape, but the cosine function is

¼

2 units left of the sine function.

Use the graphing package to graph y= cosx and

y= sin

¡

x+¼ 2

¢

on the same set of axes.

You should observe that cosx= sin

¡

x+¼ 2

¢

THE GENERAL COSINE FUNCTION

Thegeneral cosine functionis y=acosbx+c where a> 0 , b> 0.

Since the cosine function is a horizontal translation of the sine function, the constantsa,b,

andchave the same effects as for the general sine function. Click on the icon to check this.

Theprincipal axisof the general cosine function is y=c.

Theperiodof the general cosine function is

2 ¼

b

Theamplitudeof the general cosine function isa.

C The cosine function

cyan magenta yellow black

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_09\236CamAdd_09.cdr Friday, 4 April 2014 1:11:03 PM BRIAN