Understanding Engineering Mathematics

A

s

q

Figure 6.1Radians, arc, sectors.

Solution to review question 6.1.1

A. (i) 90°=

90

180

×π=

π

2

radians

(ii) − 30 °=−

30

180

×π=−

π

6

radians

(iii) 45°=

45

180

×π=

π

4

radians

(iv) 270°=

270

180

×π=

3

2

πradians

(v) 60°=

60

180

×π=

π

3

radians

B. (i)

5 π

6

radians=

5 π

6

×

180

π

= 150 °

(ii)

3 π

2

radians=

3 π

2

×

180

π

= 270 °

(iii) −

7 π

4

radians=−

7 π

4

×

180

π

=− 315 °

(iv) 4πradians= 4 π×

180

π

= 720 °

(v)−

2 π

3

radians=−

2 π

3

×

180

π

=− 120 °

C. (i) Length of arcs=rθ,θin radians.

30 °= 30 °×

π

180

=

π

6

radians

Sos= 2 ×

π

6

=

π

3

(ii) Area of sectorA=

1

2

r^2 θ=

1

2

· 22 ·

π

6

=

π

3

6.2.2 Definition of the trig ratios

➤

171 194➤

IfABCis the right-angled triangle, shown in Figure 6.2, then thetrigonometric ratios
are defined by: