View source for A-level Mathematics/OCR/C4/Formulae

==Formulae==

By the end of this module you will be expected to have learnt the following formulae:

===Differentiation===
: If <math>y = \sin kx,\,</math> then <math>\frac{dy}{dx} = k\cos kx</math>.
: If <math>y = \cos kx,\,</math> then <math>\frac{dy}{dx} = -k\sin kx</math>.

===Integration===
: <math> \int \cos kx\, dx = \frac{1}{k}\sin kx +c </math>
: <math> \int \sin kx\, dx = -\frac{1}{k}\cos kx +c </math>
: <math> \int f^'[g(x)].g^'(x)\, dx = f[g(x)] +c </math>
===Vectors===
: <math> \left| x\mathbf{i}+y\mathbf{j}+z\mathbf{k} \right| = \sqrt{x^2+y^2+z^2} </math>
: <math>(a\mathbf{i}+b\mathbf{j}+c\mathbf{k})\cdot(x\mathbf{i}+y\mathbf{j}+z\mathbf{k})=ax+by+cz</math>
: <math> \mathbf{a}\cdot\mathbf{b} = \left|\mathbf{a}\right|\left|\mathbf{b}\right|\cos \theta </math>
: The vector equation of a line through point <math>\mathbf{a}</math> with direction <math>\mathbf{b}</math> is <math>\mathbf{r} = \mathbf{a} + t\mathbf{b}</math>

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