Casa Petra - Eventos Exclusivos em São Paulo SP - /blog/page/6/

$x\; =\; r\; \backslash \backslash cos\; (\backslash \backslash phi)$

$y\; =\; r\; \backslash \backslash sin\; (\backslash \backslash phi)$

$r\; =\; \backslash \backslash sqrt\{x^2\; +\; y^2\}$ (como no [[Teorema de Pit\u00e1goras]] ou na [[Norma (matem\u00e1tica)#Normas em espa\u00e7os de dimens\u00e3o finita|norma euclidiana]]), e

$\backslash \backslash varphi\; =\; \backslash \backslash operatorname\{atan2\}(y,\; x)$

$r^2\; -\; 2\; r\; r\_0\; \backslash \backslash cos(\backslash \backslash phi\; -\; \backslash \backslash gamma)\; +\; r\_0^2\; =\; a^2$

$r(\backslash \backslash phi)=a$

$r\; =\; 2\; a\backslash \backslash cos(\backslash \backslash phi\; -\; \backslash \backslash gamma)$.

$r\; =\; r\_0\; \backslash \backslash cos(\backslash \backslash phi\; -\; \backslash \backslash gamma)\; +\; \backslash \backslash sqrt\{a^2\; -\; r\_0^2\; \backslash \backslash sin^2(\backslash \backslash phi\; -\; \backslash \backslash gamma)\}$,

$r(\backslash \backslash phi)\; =\; a\; \backslash \backslash cos\; (k\backslash \backslash phi\; +\; \backslash \backslash gamma\_0)$

$\backslash \backslash phi\; =\; \backslash \backslash gamma$,

$r(\backslash \backslash phi)\; =\; \{r\_0\}\backslash \backslash sec(\backslash \backslash phi-\backslash \backslash gamma)$.

$r(\backslash \backslash phi)\; =\; a+b\backslash \backslash phi$

$r\; =\; \backslash \backslash frac\{l\}\{1-e\backslash \backslash cos(\backslash \backslash phi)\}$

$z\; =\; x\; +\; iy$

$z\; =\; r\backslash \backslash cdot(\backslash \backslash cos\backslash \backslash varphi+i\backslash \backslash sin\backslash \backslash varphi)$

$z\; =\; re^\{i\backslash \backslash varphi\}$

$r\_0\; e^\{i\backslash \backslash varphi\_0\}\; \backslash \backslash cdot\; r\_1\; e^\{i\backslash \backslash varphi\_1\}=r\_0\; r\_1\; e^\{i(\backslash \backslash varphi\_0\; +\; \backslash \backslash varphi\_1)\}$

$\backslash \backslash frac\{r\_0\; e^\{i\backslash \backslash varphi\_0\}\}\{r\_1\; e^\{i\backslash \backslash varphi\_1\}\}=\backslash \backslash frac\{r\_0\}\{r\_1\}e^\{i(\backslash \backslash varphi\_0\; -\; \backslash \backslash varphi\_1)\}$

$(re^\{i\backslash \backslash varphi\})^n=r^ne^\{in\backslash \backslash varphi\}$

,

,

$\backslash \backslash frac\{dy\}\{dx\}=\backslash \backslash frac\{r\text{'}(\backslash \backslash phi)\backslash \backslash sin(\backslash \backslash phi)+r(\backslash \backslash phi)\backslash \backslash cos(\backslash \backslash phi)\}\{r\text{'}(\backslash \backslash phi)\backslash \backslash cos(\backslash \backslash phi)-r(\backslash \backslash phi)\backslash \backslash sin(\backslash \backslash phi)\}$

$L\; =\; \backslash \backslash int\_a^b\; \backslash \backslash sqrt\{\; \backslash \backslash left[r(\backslash \backslash phi)\backslash \backslash right]^2\; +\; \backslash \backslash left[\; \{\backslash \backslash tfrac\{dr(\backslash \backslash phi)\; \}\{\; d\backslash \backslash phi\; \}\}\; \backslash \backslash right]\; ^2\; \}\; d\backslash \backslash phi$

$\backslash \backslash frac12\backslash \backslash int\_a^b\; \backslash \backslash left(r(\backslash \backslash phi)\backslash \backslash right)^2\backslash \backslash ,\; d\backslash \backslash phi$

$\backslash \backslash left(r(\backslash \backslash phi\_i)\backslash \backslash right)^2\; \backslash \backslash pi\; \backslash \backslash cdot\; \backslash \backslash frac\{\backslash \backslash Delta\; \backslash \backslash phi\}\{2\backslash \backslash pi\}\; =\; \backslash \backslash frac\{1\}\{2\}\backslash \backslash left(r(\backslash \backslash phi\_i)\backslash \backslash right)^2\; \backslash \backslash Delta\; \backslash \backslash phi$

$\backslash \backslash sum\_\{i=1\}^n\; \backslash \backslash frac\{1\}\{2\}r(\backslash \backslash phi\_i)^2\backslash \backslash ,\backslash \backslash Delta\backslash \backslash phi$

$dA\; =\; dx\; \backslash \backslash times\; dy\backslash \backslash \; =\; J\backslash \backslash times\; dr\backslash \backslash times\; d\backslash \backslash phi\; =\; r\; \backslash \backslash times\; dr\backslash \backslash times\; d\backslash \backslash phi$

$\backslash \backslash iint\_R\; f(x,y)\; \backslash \backslash ,\; dA\; =\; \backslash \backslash int\_a^b\; \backslash \backslash int\_0^\{r(\backslash \backslash phi)\}\; f(r,\backslash \backslash phi)\backslash \backslash ,r\backslash \backslash ,dr\backslash \backslash ,d\backslash \backslash phi$

$\backslash \backslash int\_\{-\backslash \backslash infty\}^\backslash \backslash infty\; e^\{-x^2\}\; \backslash \backslash ,\; dx\; =\; \backslash \backslash sqrt\backslash \backslash pi$

$\backslash \backslash hat\{r\}=(\backslash \backslash cos(\backslash \backslash phi),\backslash \backslash sin(\backslash \backslash phi))$

$\backslash \backslash hat\backslash \backslash phi\; =\; (-\backslash \backslash sin(\backslash \backslash phi),\backslash \backslash cos(\backslash \backslash phi))\; =\; \backslash \backslash hat\{k\}\backslash \backslash times\; \backslash \backslash hat\{r\}$

$r\; =(x,y)\; =\; r(\backslash \backslash cos(\backslash \backslash phi),\backslash \backslash sin(\backslash \backslash phi))=r\backslash \backslash times\backslash \backslash hat\{r\}$

$\backslash \backslash dot\{r\}=(\backslash \backslash dot\{x\},\backslash \backslash dot\{y\})\; =\; \backslash \backslash dot\{r\}(\backslash \backslash cos(\backslash \backslash phi),\backslash \backslash sin(\backslash \backslash phi))+r\backslash \backslash dot\{\backslash \backslash phi\}(-\backslash \backslash sin(\backslash \backslash phi),\backslash \backslash cos(\backslash \backslash phi))=\backslash \backslash dot\{r\}\backslash \backslash hat\{r\}+r\backslash \backslash dot\{\backslash \backslash phi\}\backslash \backslash hat\{\backslash \backslash phi\}$