Cambridge International AS and A Level Mathematics Pure Mathematics 1

Trigonometry

P1^

7

Positive and negative angles

Unless given in the form of bearings, angles are measured from the x axis (see

figure 7.8). Anticlockwise is taken to be positive and clockwise to be negative.

ExAmPlE 7.2 In the diagram, angles ADB and CBD are right angles, angle BAD = 60°, AB = 2l

and BC = 3l.

Find the angle θ.

60°

D

C

A

B

2 l

3 l

θ

Figure 7.9

SOlUTION

First, find an expression for BD.

In triangle ABD, BD

AB

= sin 60°

⇒ BD = 2 l sin 60°

=×

=

2 3

2

3

l

l

an angle of +135°

x

an angle of –30°

x

Figure 7.8

AB = 2 l