Everything Maths Grade 11

17.5 CHAPTER 17. TRIGONOMETRY

17.5 Sine and Cosine Identities

EMBDM

There are a few identities relating to the trigonometric functions thatmake working with triangles easier. These are:

the sine rule

the cosine rule

the area rule

and will be described and applied in this section.

The Sine Rule EMBDN

DEFINITION: The Sine Rule

The sine rule applies toany triangle:

sinAˆ a

=

sinBˆ b

=

sinCˆ c

where a is the side oppositeAˆ, b is the side oppositeBˆ and c is the side oppositeCˆ.

Consider�ABC.

� � A

� B

�

C

h b a

c

The area of�ABC can be written as:

area�ABC =

1

2

c. h.

However, h can be calculated in terms ofAˆ orBˆ as:

sinAˆ = h b ∴ h = b. sinAˆ and

sinBˆ = h a ∴ h = a. sinBˆ