Fórmulas trigonométricas

Fórmulas para trabalhar com as funções trigonométricas.

Fórmulas básicas

$$\begin{array}{rcl}{\mathrm{sen}}^2(x)+{\cos }^2(x)& =& 1\\ \mathrm{tg}(x)\cdot \mathrm{cotg}(x)& =& 1\\ \mathrm{sen}(x)& =& \cos (x-\frac{\pi }{2})\\ \cos (x)& =& \mathrm{sen}(x+\frac{\pi }{2})\\ \mathrm{cotg}(x)& =& \mathrm{tg}(-x+\frac{\pi }{2})\end{array}$$

Expressão da tangente e da cotangente

$$\begin{array}{rcl}\mathrm{tg}(x)& =& \frac{\mathrm{sen}(x)}{\cos (x)}\\ \mathrm{cotg}(x)& =& \frac{\cos (x)}{\mathrm{sen}(x)}\end{array}$$

Funções de argumento 2x e x/2

$$\begin{array}{rcl}\mathrm{sen}(2x)& =& 2\mathrm{sen}(x)\cos (x)\\ \cos (2x)& =& {\cos }^2(x)-{\mathrm{sen}}^2(x)\\ |\mathrm{sen}(\frac{x}{2})|& =& \sqrt{\frac{1-\cos (x)}{2}}\\ |\cos (\frac{x}{2})|& =& \sqrt{\frac{1+\cos (x)}{2}}\end{array}$$

Fórmulas de adição

$$\begin{array}{rcl}\mathrm{sen}(x+y)& =& \mathrm{sen}(x)\cos (y)+\cos (x)\mathrm{sen}(y)\\ \mathrm{sen}(x-y)& =& \mathrm{sen}(x)\cos (y)-\cos (x)\mathrm{sen}(y)\\ \cos (x+y)& =& \cos (x)\cos (y)-\mathrm{sen}(x)\mathrm{sen}(y)\\ \cos (x-y)& =& \cos (x)\cos (y)+\mathrm{sen}(x)\mathrm{sen}(y)\end{array}$$