Cambridge International Mathematics

Example 1 Self Tutor

a State the exact coordinates of:

i A ii B

b Find the coordinates of:

i A ii B

correct to 3 decimal places.

aiA(cos 152o,sin 152o) ii B(cos 297o,sin 297o)

biA(¡ 0 : 883 , 0 :469) ii B(0: 454 ,¡ 0 :891)

Example 2 Self Tutor

a Find the size of angle AOP marked with an

arrow.

b Find the coordinates of P using:

i the unit circle

ii symmetry in they-axis.

c What can be deduced fromb?

d Usecto simplify tan(180o¡μ).

y

x

(-1 ¡0, ) ()1 ¡0,

(0,-1)

(0 ),¡1

10°

20°

30°

40°

50°

60°

70°

110°100° 80°

120°

130°

140°

150°

160°

170°

180°

190°

200°

210°

220°

230°

240°

250°

260° 270°280° 290°

300°

310°

320°

330°

340°

350°

-0 5. 0 5.

-0 5.

0 5.

Below is a unit circle diagram from which we can estimate trigonometric ratios.

x

y

O 1

1

-1

-1

297°

B

A 152°152°

x

y

O

q

1

A

1

-1

-1

P

q

()cos , sin¡q ¡ ¡q

580 Further trigonometry (Chapter 29)

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Y:\HAESE\IGCSE01\IG01_29\580IGCSE01_29.CDR Monday, 27 October 2008 2:52:29 PM PETER