Cambridge International Mathematics

316 Trigonometry (Chapter 15)

Triangle AB BC AC

AB

AC

BC

AC

BC

AB

1

2

3

4

Convert all fractions to 2 decimal places.

2 Repeat 1 for the set of triangles alongside.

3 What have you discovered from 1 and 2?

Notice that

AB

AC

=

ADJ

HYP

,

BC

AC

=

OPP

HYP

and

BC

AB

=

OPP

ADJ

.

From theDiscoveryyou should have found that:

For a fixed angled right angled triangle, the ratios

OPP

HYP

,

ADJ

HYP

and

OPP

ADJ

are

constant no matter how much the triangle is enlarged.

For a particular angle of a right angled triangle the ratios

OPP

HYP

,

ADJ

HYP

and

OPP

ADJ

are fixed.

These ratios have the traditional namessine,cosineandtangentrespectively.

We abbreviate them tosin,cosandtan.

Notice that

sinμ

cosμ

= sinμ¥cosμ=

OPP

HYP

£

HYP

ADJ

=

OPP

ADJ

= tanμ

So, tanμ=

sinμ

cosμ

We can use these ratios to find unknown sides and angles of right angled triangles.

B THE TRIGONOMETRIC RATIOS [8.1]

A B 1

C 1

B 2

C 2

B 3

C 3

B 4

C 4

PRINTABLE

WORKSHEET

In any right angled triangle with one angleμwe have:

sinμ=

OPP

HYP

, cosμ=

ADJ

HYP

, tanμ=

OPP

ADJ A μ B

C

OPP

ADJ

HYP

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Y:\HAESE\IGCSE01\IG01_15\316IGCSE01_15.CDR Tuesday, 7 October 2008 2:03:45 PM PETER