Six Trig Functions

Base Case

Definite Integral

Indefinite Integral

$f\prime \left(x\right)=\mathit{cos}\left(x\right)$

$\underset{a}{\overset{b}{\int }}\mathit{cos}\left(x\right) \mathit{dx}\mathit{=}{\mathit{sin}\left(x\right)|}_{x=a}^{x=b}$

$\int \mathit{cos}\left(x\right) \mathit{dx}\mathit{=}\mathit{sin}\left(x\right)\mathit{+}\mathit{C}$

$f\prime \left(x\right)=\mathit{sin}\left(x\right)$

$\underset{a}{\overset{b}{\int }}\mathit{sin}\left(x\right) \mathit{dx}\mathit{=}{–\mathit{cos}\left(x\right)|}_{x=a}^{x=b}$

$\int \mathit{sin}\left(x\right) \mathit{dx}\mathit{=}–\mathit{cos}\left(x\right)\mathit{+}\mathit{C}$

$f\prime \left(x\right)={\mathit{sec}}^2\left(x\right)$

$\underset{a}{\overset{b}{\int }}{\mathit{sec}}^2\left(x\right) \mathit{dx}\mathit{=}{\mathit{tan}\left(x\right)|}_{x=a}^{x=b}$

$\int {\mathit{sec}}^2\left(x\right) \mathit{dx}\mathit{=}\mathit{tan}\left(x\right)\mathit{+}\mathit{C}$

$f\prime \left(x\right)=\mathit{sec}\left(x\right)\mathit{tan}\left(x\right)$

$\underset{a}{\overset{b}{\int }}\mathit{sec}\left(x\right)\mathit{tan}\left(x\right) \mathit{dx}\mathit{=}{\mathit{sec}\left(x\right)|}_{x=a}^{x=b}$

$\int \mathit{sec}\left(x\right)\mathit{tan}\left(x\right) \mathit{dx}\mathit{=}\mathit{sec}\left(x\right)\mathit{+}\mathit{C}$

$f\prime \left(x\right)=–\mathit{csc}\left(x\right)\mathit{cot}\left(x\right)$

$\underset{a}{\overset{b}{\int }}–\mathit{csc}\left(x\right)\mathit{cot}\left(x\right) \mathit{dx}\mathit{=}{\mathit{csc}\left(x\right)|}_{x=a}^{x=b}$

$\int –\mathit{csc}\left(x\right)\mathit{cot}\left(x\right) \mathit{dx}\mathit{=}\mathit{csc}\left(x\right)\mathit{+}\mathit{C}$

$f\prime \left(x\right)={–\mathit{csc}}^2\left(x\right)$

$\underset{a}{\overset{b}{\int }}{–\mathit{csc}}^2\left(x\right) \mathit{dx}\mathit{=}{\mathit{cot}\left(x\right)|}_{x=a}^{x=b}$

$\int {–\mathit{csc}}^2\left(x\right) \mathit{dx}\mathit{=}\mathit{cot}\left(x\right)\mathit{+}\mathit{C}$