Cambridge International Mathematics

Trigonometry (Chapter 15) 327

27 In the triangle alongside, P is 5 m from each of the

vertices. Find the length of each side of the triangle.

Theunit circleis the circle with centre O(0,0)

and radius 1 unit.

Consider point P(a,b) in the first quadrant.

Notice that sinμ=

b

1

=b and cosμ=

a

1

=a

So, P has coordinates (cosμ,sinμ):

Example 9 Self Tutor

a State exactly the coordinates of

point P.

b Find the coordinates of P correct

to 3 decimal places.

a Pis(cos 72o,sin 72o) b Pis(0: 309 , 0 :951)

EXERCISE 15D.1

1 If angle TOP measures 28 oand angle TOQ measures 68 o,

find:

a the exact coordinates of P and Q

b the coordinates of P and Q correct to 3 decimal places.

THE FIRST QUADRANT OF THE

UNIT CIRCLE [8.2]

D

80°

60° 40°

P

A

C B

y

O x

q

a

b

P,()ab¡

1

1

-1

-1 N

1

y

x

O

(^1) P
-1
-1 1
72°
y
x
O
(^1) Q
-1
-1 1
P
T
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Y:\HAESE\IGCSE01\IG01_15\327IGCSE01_15.CDR Tuesday, 7 October 2008 2:12:49 PM PETER