Cambridge International Mathematics

Trigonometry (Chapter 15) 319

de f

gh i

jk l

4 Findallthe unknown angles and sides of:

abc

FINDING ANGLES

In the right angled triangle shown, sinμ=^35 :

So, we are looking for the angleμwith a sine of^35.

If sin¡^1 (::::::) reads “the angle with a sine of ......”, we can write μ= sin¡^1

¡ 3

5

¢

.

Another way of describing this is to say “μis theinverse sineof^35 ”.

If sinμ=x thenμis theinverse sineofx.

You can find graphics calculator instructions for finding these inverse trigonometric functions on page 16.

We can defineinverse cosineandinverse tangentin a similar way.

Example 5 Self Tutor

Find the measure of the angle markedμin:

ab

28°

xm

52 m 68°

xkm

45 km

74°

xcm

80 cm

27°

xmm

11 mm

42°

xkm

5km

70°

xcm

5.6 cm 50°

xm 27 m

49°

xkm

12 km

34°

8m xm

q

28°

bcm

12 cm

acm

am bm

15 m

63°

q

25°

acm

45 cm bcm

q

q

5cm

3cm

HYP

OPP

7m

4m

q

2.67 km

5.92 km

q

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Y:\HAESE\IGCSE01\IG01_15\319IGCSE01_15.CDR Friday, 26 September 2008 2:52:08 PM PETER