The Sine and Cosine Rule GCSE revision and worksheets

What you need to know:

The sine and cosine rules are an extension of the trigonometry we know, and they allow us to find information about triangles that don’t have to be right-angled. They are both expressed according the way the following triangle is labelled, with the letter of each angle corresponding to the side opposite to it.

Then, sine rule is:

\dfrac{\sin A}{a} = \dfrac{\sin B}{b} = \dfrac{\sin C}{c}

and the cosine rule is:

a^2 = b^2 + c^2 - 2bc cos (A)

You are required to know how to use these formulae to find both angles and sides. You can either choose to memorise them and then rearrange appropriately in the exam if needed (for the sine rule this is easy, for the cosine rule perhaps less so), or you can choose to memorise the equations in both of their required forms. It’s completely up to you as long as you know how, and just as importantly when, to use them. In terms of the “when”, they both require specific set-ups to be usable, and you might not be told explicitly to use one or the other in the exam, so you should practise questions on this topic enough to know when one is appropriate over the other.

Additionally, you should be aware of the “ambiguous case of the sine rule”, whereby there are sometimes two answers you could get for an angle (one obtuse, one acute) when using the sine rule, and they’re both correct. Watch out for if the question asks for one specifically.