IMPORTANT: This website is no longer being updated, these notes are (at least) 3 years old and may not be relevant to current specifications. They are provided to be helpful only!

Compound angle formulae

Posted in Maths, Core 4

There are 6 compound-angle formulae you need to be aware of. Depending on your exam board you may or may not be required to remember these as they may be in your formula books.

Dynamic image 0

Dynamic image 1


Dynamic image 2

Dynamic image 3


Dynamic image 4

Dynamic image 5


Where Dynamic image 6 and Dynamic image 7 are just any angle.

These can be used to expand and simplify expressions involving trigonometric functions.

Double angle formulae

By substituting Dynamic image 8 into the compound formulae gives expressions for Dynamic image 9, Dynamic image 10 and Dynamic image 11:

Dynamic image 12


Dynamic image 13

Dynamic image 14

Dynamic image 15


Dynamic image 16

Example usage

These can be used to solve equations involving trigonometric functions.

Example question: Find the smallest value of Dynamic image 6, such that Dynamic image 18

Worked solution: Firstly use the above relation for Dynamic image 9 and substitute it into the equation:

Dynamic image 20

Divide both sides by Dynamic image 21 to elimate it the from the equation:

Dynamic image 22

Divide by 4...

Dynamic image 23