A Funciones e identidades básicas

Gráficos de funciones matriz

Gráficos de las funciones trigonométricas

Identidades trigonométricas

Identidades de Pitágoras	$\begin{array}{l}{\cos }^2\theta +{\mathrm{sen}}^2\theta =1\\ 1+{\tan }^2\theta ={\sec }^2\theta \\ 1+{\cot }^2\theta ={\csc }^2\theta \end{array}$
Identidades par-impar	$\begin{array}{l}\cos (-\theta )=\cos \theta \hfill \\ \sec (-\theta )=\sec \theta \hfill \\ \mathrm{sen}(-\theta )=-\mathrm{sen}\theta \hfill \\ \tan (-\theta )=-\tan \theta \hfill \\ \csc (-\theta )=-\csc \theta \hfill \\ \cot (-\theta )=-\cot \theta \hfill \end{array}$
Identidades de la cofunción	$\begin{array}{l}\cos \theta =\mathrm{sen}\left(\frac{\pi }{2}-\theta \right)\hfill \\ \mathrm{sen}\theta =\cos \left(\frac{\pi }{2}-\theta \right)\hfill \\ \tan \theta =\cot \left(\frac{\pi }{2}-\theta \right)\hfill \\ \cot \theta =\tan \left(\frac{\pi }{2}-\theta \right)\hfill \\ \sec \theta =\csc \left(\frac{\pi }{2}-\theta \right)\hfill \\ \csc \theta =\sec \left(\frac{\pi }{2}-\theta \right)\hfill \end{array}$
Identidades fundamentales	$\begin{array}{l}\tan \theta =\frac{\mathrm{sen}\theta }{\cos \theta }\hfill \\ \sec \theta =\frac{1}{\cos \theta }\hfill \\ \csc \theta =\frac{1}{\mathrm{sen}\theta }\hfill \\ \text{cot}\theta =\frac{1}{\text{tan}\theta }=\frac{\text{cos}\theta }{\text{sen}\theta }\hfill \end{array}$
Identidades de suma y resta	$\begin{array}{l}\cos (\alpha +\beta )=\cos \alpha \cos \beta -\mathrm{sen}\alpha \mathrm{sen}\beta \hfill \\ \cos (\alpha -\beta )=\cos \alpha \cos \beta +\mathrm{sen}\alpha \mathrm{sen}\beta \hfill \\ \mathrm{sen}(\alpha +\beta )=\mathrm{sen}\alpha \cos \beta +\cos \alpha \mathrm{sen}\beta \hfill \\ \mathrm{sen}(\alpha -\beta )=\mathrm{sen}\alpha \cos \beta -\cos \alpha \mathrm{sen}\beta \hfill \\ \tan (\alpha +\beta )=\frac{\tan \alpha +\tan \beta }{1-\tan \alpha \tan \beta }\hfill \\ \tan (\alpha -\beta )=\frac{\tan \alpha -\tan \beta }{1+\tan \alpha \tan \beta }\hfill \end{array}$
Fórmulas del ángulo doble	$\begin{array}{l}\mathrm{sen}(2\theta )=2\mathrm{sen}\theta \cos \theta \hfill \\ \cos (2\theta )={\cos }^2\theta -{\mathrm{sen}}^2\theta \hfill \\ \cos (2\theta )=1-2{\mathrm{sen}}^2\theta \hfill \\ \cos (2\theta )=2{\cos }^2\theta -1\hfill \\ \tan (2\theta )=\frac{2\tan \theta }{1-{\tan }^2\theta }\hfill \end{array}$
Fórmulas de medio ángulo	$\begin{array}{l}\mathrm{sen}\frac{\alpha }{2}=\pm \sqrt{\frac{1-\cos \alpha }{2}}\hfill \\ \cos \frac{\alpha }{2}=\pm \sqrt{\frac{1+\cos \alpha }{2}}\hfill \\ \tan \frac{\alpha }{2}=\pm \sqrt{\frac{1-\cos \alpha }{1+\cos \alpha }}\hfill \\ \tan \frac{\alpha }{2}=\frac{\mathrm{sen}\alpha }{1+\cos \alpha }\hfill \\ \tan \frac{\alpha }{2}=\frac{1-\cos \alpha }{\mathrm{sen}\alpha }\hfill \end{array}$
Fórmulas de reducción	$\begin{array}{l}{\mathrm{sen}}^2\theta =\frac{1-\cos \left(2\theta \right)}{2}\\ {\cos }^2\theta =\frac{1+\cos \left(2\theta \right)}{2}\\ {\tan }^2\theta =\frac{1-\cos \left(2\theta \right)}{1+\cos \left(2\theta \right)}\end{array}$
Fórmulas producto a suma	$\begin{array}{l}\cos \alpha \cos \beta =\frac{1}{2}\left[\cos (\alpha -\beta )+\cos (\alpha +\beta )\right]\hfill \\ \mathrm{sen}\alpha \cos \beta =\frac{1}{2}\left[\mathrm{sen}(\alpha +\beta )+\mathrm{sen}(\alpha -\beta )\right]\hfill \\ \mathrm{sen}\alpha \mathrm{sen}\beta =\frac{1}{2}\left[\cos (\alpha -\beta )-\cos (\alpha +\beta )\right]\hfill \\ \cos \alpha \mathrm{sen}\beta =\frac{1}{2}\left[\mathrm{sen}(\alpha +\beta )-\mathrm{sen}(\alpha -\beta )\right]\hfill \end{array}$
Fórmulas de suma a producto	$\begin{array}{l}\mathrm{sen}\alpha +\mathrm{sen}\beta =2\mathrm{sen}\left(\frac{\alpha +\beta }{2}\right)\cos \left(\frac{\alpha -\beta }{2}\right)\hfill \\ \mathrm{sen}\alpha -\mathrm{sen}\beta =2\mathrm{sen}\left(\frac{\alpha -\beta }{2}\right)\cos \left(\frac{\alpha +\beta }{2}\right)\hfill \\ \cos \alpha -\cos \beta =-2\mathrm{sen}\left(\frac{\alpha +\beta }{2}\right)\mathrm{sen}\left(\frac{\alpha -\beta }{2}\right)\hfill \\ \cos \alpha +\cos \beta =2\cos \left(\frac{\alpha +\beta }{2}\right)\cos \left(\frac{\alpha -\beta }{2}\right)\hfill \end{array}$
Ley de senos	$\begin{array}{l}\frac{\mathrm{sen}\alpha }{a}=\frac{\mathrm{sen}\beta }{b}=\frac{\mathrm{sen}\gamma }{c}\hfill \\ \frac{a}{\mathrm{sen}\alpha }=\frac{b}{\mathrm{sen}\beta }=\frac{c}{\mathrm{sen}\gamma }\hfill \end{array}$
Ley de cosenos	$\begin{array}{l}{a}^2=b^2+c^2-2bc\cos \alpha \hfill \\ b^2=a^2+c^2-2ac\cos \beta \hfill \\ c^2=a^2+b^2-2ab\text{cos}\gamma \hfill \end{array}$

Tabla A1