A-level Mathematics/OCR/C4/Formulae

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

If ${\displaystyle y=\sin kx,\,}$ then ${\displaystyle {\frac {dy}{dx}}=k\cos kx}$.

If ${\displaystyle y=\cos kx,\,}$ then ${\displaystyle {\frac {dy}{dx}}=-k\sin kx}$.

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

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

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

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

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

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

The vector equation of a line through point ${\displaystyle \mathbf {a} }$ with direction ${\displaystyle \mathbf {b} }$ is ${\displaystyle \mathbf {r} =\mathbf {a} +t\mathbf {b} }$