Sine and Cosine Formulae

sin x = sin (180 – x)
e.g. sin 130 = sin (180 – 130) = sin 50

cos x = -cos (180 – x)

The Sine Rule:
This works in any triangle:

 a    =    b    =    c  
sinA     sinB      sinC

alternatively, sinA = sinB = sinC
a        b       c

NOTE: the triangle is labelled as follows:

sine_a10

The Cosine Rule:
c² = a² + b² – 2abcosC
can also be written as:
a² = b² + c² – 2bccosA

This also works in any triangle.

 

The area of a triangle
The area of any triangle is ½ absinC (using the above notation)
This formula is useful if you don’t know the height of a triangle (since you need to know the height for ½ base × height).