Cambridge International Mathematics

Trigonometry (Chapter 15) 329

8aIfμis any acute angle as shown, find the length of:

i OQ ii PQ iii AT

b Explain howtanμor tangentμmay have been given its

name.

IMPORTANT ANGLES

From the previous exercise you should have discovered trigonometric ratios of some important angles:

μ cosμ sinμ tanμ

0 o 1 0 0

30 o

p

3

2

1

2

p^1

3

45 o p^12 p^121

60 o^12

p

3

2

p

3

90 o 0 1 undefined

In the following exercise you will see some new notation. It is customary to write:

sin^2 μ to represent (sinμ)^2 , cos^2 μ to represent (cosμ)^2 , and tan^2 μ to represent (tanμ)^2.

EXERCISE 15D.2

1 Show that:

a sin^230 o+ cos^230 o=1 b cos^245 o+ sin^245 o=1

c sin 30ocos 60o+ sin 60ocos 30o=1 d sin^230 o+ sin^245 o+ sin^260 o=^32

2 Without using a calculator find the value of:

a sin^260 o b

sin 30o

cos 30o

c tan^260 o

d cos 0o+ sin 90o e cos^230 o f 1 ¡tan^230 o

g

sin 60o

cos 60o

h 1 ¡cos 60o i 2 + sin 30o

3 Find the exact value of the unknown in:

abc

de f

You should memorise

these results or be

able to quickly

deduce them from

diagrams.

12 cm 60°

acm

10 cm

30°

hcm

cm

8m

60°

120° 15 cm

dcm

xcm

6cm

60°

~` 2 cm

45°

ycm

x

1

Q A(1, 0)

1

y

P T

q

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Y:\HAESE\IGCSE01\IG01_15\329IGCSE01_15.CDR Friday, 17 October 2008 4:09:54 PM PETER