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$\frac{\mathrm{d}}{dx}(\cos^{-1}{x})$,$\frac{\mathrm{d}}{dx}(\cos^{-1}{x})=-\frac{1}{\sqrt{1-x^2}}$

$\frac{\mathrm{d}}{dx}(\cot^{-1}{x})$,$\frac{\mathrm{d}}{dx}(\cot^{-1}{x})=-\frac{1}{1+x^2}$

$\frac{\mathrm{d}}{dx}(\csc^{-1}{x})$,$\frac{\mathrm{d}}{dx}(\csc^{-1}{x})=-\frac{1}{x\sqrt{x^2-1}}$

$\frac{\mathrm{d}}{dx}(\sec^{-1}{x})$,$\frac{\mathrm{d}}{dx}(\sec^{-1}{x})=\frac{1}{x\sqrt{x^2-1}}$

$\frac{\mathrm{d}}{dx}(\sin^{-1}{x})$,$\frac{\mathrm{d}}{dx}(\sin^{-1}{x})=\frac{1}{\sqrt{1-x^2}}$

$\frac{\mathrm{d}}{dx}(\tan^{-1}{x})$,$\frac{\mathrm{d}}{dx}(\tan^{-1}{x})=\frac{1}{1+x^2}$

$\frac{\mathrm{d}}{dx}(\cos{x})$,$\frac{\mathrm{d}}{dx}(\cos{x})=-\sin{x}$

$\frac{\mathrm{d}}{dx}(\cot{x})$,$\frac{\mathrm{d}}{dx}(\cot{x})=-\csc^{2}{x}$

$\frac{\mathrm{d}}{dx}(\csc{x})$,$\frac{\mathrm{d}}{dx}(\csc{x})=-\csc{x}\cot{x}$

$\frac{\mathrm{d}}{dx}(\sec{x})$,$\frac{\mathrm{d}}{dx}(\sec{x})=\sec{x}\tan{x}$

$\frac{\mathrm{d}}{dx}(\sin{x})$,$\frac{\mathrm{d}}{dx}(\sin{x})=\cos{x}$

$\frac{\mathrm{d}}{dx}(\tan{x})$,$\frac{\mathrm{d}}{dx}(\tan{x})=\sec^{2}{x}$

$\int\frac{1}{x}dx$,$\int\frac{1}{x}dx=\ln|x|+C$

$\int\cos(ax)dx$,$\int\cos(ax)dx=\frac{1}{a}\sin(ax)$

$\int\cos{x}dx$,$\int\cos{x}dx=\sin{x}+C$

$\int\cot{x}dx$,$\int\cot{x}dx=\ln|\sin{x}|+C$

$\int\csc^{2}{x}dx$,$\int\csc^{2}{x}dx=-\cot{x}+C$

$\int\csc{x}dx$,$\int\csc{x}dx=\ln|\csc{x}-\cot{x}|+C$

$\int\csc{x}\cot{x}dx$,$\int\csc{x}\cot{x}dx=-\csc{x}+C$

$\int\sec^{2}{x}dx$,$\int\sec^{2}{x}dx=\tan{x}+C$

$\int\sec{x}dx$,$\int\sec{x}dx=\ln|\sec{x}+\tan{x}|+C$

$\int\sec{x}\tan{x}dx$,$\int\sec{x}\tan{x}dx=\sec{x}+C$

$\int\sin(ax)dx$,$\int\sin(ax)dx=-\frac{1}{a}\cos(ax)+C$

$\int\sin{x}dx$,$\int\sin{x}dx=-\cos{x}+C$

$\int\tan(ax)dx$,$\int\tan(ax)dx=-\frac{1}{a}\ln(\cos{ax})+C$

$\int\tan{x}dx$,$\int\tan{x}dx=\ln|\sec{x}|+C$

$\int{u}\mathop{\mathrm{d}v}$,$\int{u}\mathop{\mathrm{d}v}=uv-\int{v}\mathop{\mathrm{d}u}$

$\cos(2x)$,$\begin{eqnarray}

\end{eqnarray}$ ,Identities Trig

$\cos^{2}{x}$,$\cos^{2}{x}=\frac{1}{2}(1+\cos(2x))$

$\cot^{2}{\theta}$,$\cot^{2}{\theta}=\csc^{2}{\theta}-1$

$\csc^{2}{\theta}$,$\csc^{2}{\theta}=1+\cot^{2}{\theta}$

$\sec^{2}{\theta}$,$\sec^{2}{\theta}=1+\tan^{2}{\theta}$

$\sin(2x)$,$\sin(2x)=2\sin{x}\cos{x}$

$\sin^{2}{x}$,$\sin^{2}{x}=\frac{1}{2}(1-\cos(2x))$

$\tan(2x)$,$\tan(2x)=\frac{2\tan{x}}{1-\tan^{2}{x}}$

$\tan^{2}{\theta}$,$\tan^{2}{\theta}=\sec^{2}{\theta}-1$

\end{array}$ ,$\begin{array}{ccc}

\end{array}$ ,Substitution Trig

\end{array}$ ,$\begin{array}{ccc}

\end{array}$ ,Substitution Trig

\end{array}$ ,$\begin{array}{ccc}

\end{array}$ ,Substitution Trig

$\sin0=\sin(2\pi)=0$,

$\cos0=\cos(2\pi)=1$,

$\tan0=\tan\pi=\tan(2\pi)=0$,

$\sin\left(\frac{\pi}{6}\right)=\frac{1}{2} $,

$\cos\left(\frac{\pi}{6}\right)=\frac{\sqrt{3} }{2} $,

$\tan\left(\frac{\pi}{6}\right)=\frac{1}{\sqrt{3} } $,

$\sin\left(\frac{\pi}{4}\right)=\frac{\sqrt{2} }{2} =\frac{1}{\sqrt{2} } $,

$\cos\left(\frac{\pi}{4}\right)=\frac{\sqrt{2} }{2} =\frac{1}{\sqrt{2} } $,

$\tan\left(\frac{\pi}{4}\right)=1$,

$\sin\left(\frac{\pi}{3}\right)=\frac{\sqrt{3} }{2} $,

$\cos\left(\frac{\pi}{3}\right)=\frac{1}{2} $,

$\tan\left(\frac{\pi}{3}\right)=\sqrt{3} $,

$\sin\left(\frac{\pi}{2}\right)=1$,

$\cos\left(\frac{\pi}{2}\right)=0$,

$\tan\left(\frac{\pi}{2}\right)=\tan\left(\frac{3\pi}{2}\right)=\mathrm{undefined} $,

$\sin\pi=0$,

$\cos\pi=-1$,

$\sin\left(\frac{3\pi}{2}\right)=-1$,

$\cos\left(\frac{3\pi}{2}\right)=0$,

$\frac{\mathrm{d}}{dx}a^x$,$\frac{\mathrm{d}}{dx}a^x=a^x\ln{a}$

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∫cos⁡(ax) dx∫cos(ax)dx