A-level Mathematics/OCR/C4/Formulae

Formulae

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

If

y=\sin kx,\,

then

{\frac {dy}{dx}}=k\cos kx

.

If

y=\cos kx,\,

then

{\frac {dy}{dx}}=-k\sin kx

.

\int \cos kx\,dx={\frac {1}{k}}\sin kx+c

\int \sin kx\,dx=-{\frac {1}{k}}\cos kx+c

\int f^{'}[g(x)].g^{'}(x)\,dx=f[g(x)]+c

\left|x\mathbf {i} +y\mathbf {j} +z\mathbf {k} \right|={\sqrt {x^{2}+y^{2}+z^{2}}}

(a\mathbf {i} +b\mathbf {j} +c\mathbf {k} )\cdot (x\mathbf {i} +y\mathbf {j} +z\mathbf {k} )=ax+by+cz

\mathbf {a} \cdot \mathbf {b} =\left|\mathbf {a} \right|\left|\mathbf {b} \right|\cos \theta

The vector equation of a line through point

\mathbf {a}

with direction

\mathbf {b}

is

\mathbf {r} =\mathbf {a} +t\mathbf {b}

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