Cambridge International Mathematics

a

sin 60o=

p

3

2

cos 60o=^12

tan 60o=

p

3

2

1

2

=

p

3

b

sin 150o=^12

cos 150o=¡

p

3

2

tan 150o=

1

2

¡

p

3

2

=¡p^13

c

sin 225o=¡p^12

cos 225o=¡p^12

tan 225o=1

EXERCISE 29A.2

1 Use a unit circle to findsinμ,cosμandtanμfor:

a μ=30o b μ= 180o c μ= 135o d μ= 210o

e μ= 300o f μ= 270o g μ= 315o h μ= 240o

sin^2 μ= (sinμ)^2 ,

cos^2 μ= (cosμ)^2

and so on.

2 Without using a calculator, find the exact values of:

a sin^2135 o b cos^2120 o c tan^2210 o d cos^3330 o

Check your answers using a calculator.

3 Use a unit circle diagram to find all angles between 0 oand 360 owhich have:

a a sine of^12 b a cosine of

p

3

2 c a sine of

p^1

2

d a sine of¡^12 e a sine of¡ 1 f a cosine of¡

p

3

2.

Consider the acute angled triangle alongside, in which the sides

opposite anglesA,BandCare labelleda,bandcrespectively.

Area of triangle ABC=^12 £AB£CN=^12 ch

But sinA=

h

b

) h=bsinA

) area=^12 c(bsinA) or^12 bcsinA

If the altitudes from A and B were drawn, we could also show that

area=^12 acsinB=^12 absinC. area=^12 absinC is worth remembering.

B AREA OF A TRIANGLE USING SINE [8.6]

AB

C

A

b h a

N c

C

B

y

x

³

1

2 ,

p

3

2

́

O

60°

y

x

150°150°

³

¡

p 3

2 ,

1

2

́

O

y

x

225°225°

³

¡p^12 ,¡p^12

́ O

Further trigonometry (Chapter 29) 583

IGCSE01

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_29\583IGCSE01_29.CDR Monday, 27 October 2008 2:52:38 PM PETER