## Content

### Formulas

A formula is a way of relating different quantities using algebra. The well-known formula

\[ A = \pi r^2 \]relates the area \(A\) of a circle to its radius \(r\). The variable \(A\) is the subject of the formula since it stands alone on the left-hand side of the equation.

It is often the case in mathematics that we need to rearrange a formula and make one of the other variables to be the subject.

For example, the cosine rule states that if \(a,b,c\) are the side lengths of a triangle and \(A\) is the angle opposite \(a\), then

\[a^2=b^2+c^2-2bc\,\cos A.\]If we wish to find the angle in a triangle, given the three side lengths, then we need to make \(\cos A\) the subject. Rearranging the terms, we have

\[2bc\,\cos A = b^2+c^2-a^2 \implies \cos A = \dfrac{b^2+c^2-a^2}{2bc}.\]Students should be well-practised in this sort of procedure.