Everything Maths Grade 11

CHAPTER 17. TRIGONOMETRY 17.3

�

D

�

A

�

B

�

C

60 ◦

30

◦

v

a

1

2 a

Figure 17.8: An equilateral triangle with one angle bisected.

So, we have:

sin(30◦) =

opposite( 30 ◦)

hypotenuse

=

a

2

a

=

1

2

cos(30◦) =

adjacent( 30 ◦)

hypotenuse

=

√ 3

2 a

a

=

√

3

2

tan(30◦) =

opposite( 30 ◦)

adjacent( 30 ◦)

=

a

√^2

3

2 a

=

1

√

3

sin(60◦) =

opposite( 60 ◦)

hypotenuse

=

√ 3

2 a

a

=

√

3

2

cos(60◦) =

adjacent( 60 ◦)

hypotenuse

=

a

2

a

=

1

2

tan(60◦) =

opposite( 60 ◦)

adjacent( 60 ◦)

=

√

3

2 a

a

2

=

√

3

Tip

Two useful triangles to

remember

30 ◦

60 ◦

1

√

3

2

45 ◦

45 ◦

1

1

√

2

You do not have to memorise these identities if you know how to work them out.

Alternate Definition fortanθ EMBDB

We know that tan θ is defined as:

tan θ =

opposite

adjacent

This can be written as:

tan θ =

opposite

adjacent

×

hypotenuse

hypotenuse

=

opposite

hypotenuse

×

hypotenuse

adjacent

But, we also know that sin θ is defined as:

sin θ =

opposite

hypotenuse