# Sine and cosine formulae

Source: https://projectalevel.co.uk/maths/trigonometry/sine_and_cosine_formulae

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**Sine and Cosine Formulae**
sin x = sin (180 - x)
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:

![](https://content.projectalevel.co.uk/img/maths/rules.gif)

**The Cosine Rule**
c² = a² + b² - 2abcosC
which 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).