Cambridge Additional Mathematics

1

1

45 °

~`2

P,(a a)

x

y

1

1

45°

45°

a

a

B

1

O

x

y

(0 1),

(1 0),

(0 -1),

(-1 0),

r_p

Ef_p

Uf_p

Tf_p

&-[[, * &[[, *

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

O

The unit circle and radian measure (Chapter 8) 217

b Describe the resulting graph. Is it the graph of a function?

c Evaluate x^2 +y^2. Hence determine the equation of this graph in terms ofxandyonly.

2 Use the graphing package to plot:

a f(x,y):x= 2 cost, y= sin(2t), 0 ± 6 t 6360 ±g

b f(x,y):x= 2 cost, y= 2 sin(3t), 0 ± 6 t 6360 ±g

c f(x,y):x= 2 cost, y= cost¡sint, 0 ± 6 t 6360 ±g

d f(x,y):x= cos^2 t+ sin 2t, y= cost, 0 ± 6 t 6360 ±g

e f(x,y):x= cos^3 t, y= sint, 0 ± 6 t 6360 ±g

Angles which are multiples of¼ 6 and¼ 4 occur frequently, so it is important for us to write their trigonometric

ratios exactly.

MULTIPLES OF¼ 4 OR 45 ±

Triangle OBP is isosceles as angle OPB

also measures 45 ±.

Letting OB=BP=a,

a^2 +a^2 =1^2 fPythagorasg

) 2 a^2 =1

) a^2 =^12

) a=p^12 fas a> 0 g

So, P is (p^12 ,p^12 ) where p^12 ¼ 0 : 707.

cos¼ 4 =p^12 and sin¼ 4 =p^12

You should remember these values. If you forget, draw a right angled

isosceles triangle with equal sides of length 1.

Formultiples of¼ 4 , we have:

E Multiples of and

¼

6

AND

¼

4

E

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_08\217CamAdd_08.cdr Friday, 4 April 2014 1:01:17 PM BRIAN