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![[tex]\left\{\begin{matrix}x^2 = y^2 + z^2\\ x^2 + y^2 = 1\end{matrix}\right.[/tex]](images/latex/bfc8e806e2241f088d44a763c03487247f009e6a_0.png "[tex]\left\{\begin{matrix}x^2 = y^2 + z^2\\ x^2 + y^2 = 1\end{matrix}\right.[/tex]")
![[tex]y=rcos \theta[/tex]](images/latex/2cb5e9b1b37e1f40bb1ef062693c6265945b76eb_0.png "[tex]y=rcos \theta[/tex]")
![[tex]z=r sen \theta[/tex]](images/latex/5c4eb3f58f20ae0dbc36964d7b83de3b54583b15_0.png "[tex]z=r sen \theta[/tex]")
![[tex]x=?[/tex]](images/latex/763cf30ef2b114d2dbadf96cf16b1f5a3301a2e7_0.png "[tex]x=?[/tex]")
![[tex]\left\{\begin{matrix}x^2 = r^2 \\ x^2 + r^2 cos ^2 \theta= 1\end{matrix}\right.[/tex]](images/latex/abd2916881670eef7ded7117cd8c7fbcb6f947f4_0.png "[tex]\left\{\begin{matrix}x^2 = r^2 \\ x^2 + r^2 cos ^2 \theta= 1\end{matrix}\right.[/tex]")
![[tex]\left\{\begin{matrix}x^2 = r^2 \\ r^2 (1+cos ^2 \theta )= 1\end{matrix}\right.[/tex]](images/latex/3b7499d0e08337d09f029f63639f156b0cd501d8_0.png "[tex]\left\{\begin{matrix}x^2 = r^2 \\ r^2 (1+cos ^2 \theta )= 1\end{matrix}\right.[/tex]")
![[tex]r=\sqrt{\frac{1}{1+ cos^2 \theta}}[/tex]](images/latex/77f996438f27e937aa22f635071807de1ef59e38_0.png "[tex]r=\sqrt{\frac{1}{1+ cos^2 \theta}}[/tex]")
![[tex]x=\sqrt{\frac{1}{1+ cos^2 \theta}}[/tex]](images/latex/18bd6461e2254ffd70cdcdd10812a9d72275eba3_0.png "[tex]x=\sqrt{\frac{1}{1+ cos^2 \theta}}[/tex]")
![[tex]y={\frac{cos}{\sqrt{1+ cos^2 \theta}}}[/tex]](images/latex/f4939826a3152bd090a89c12ff3e057f53cf7a3d_0.png "[tex]y={\frac{cos}{\sqrt{1+ cos^2 \theta}}}[/tex]")
![[tex]z={\frac{sen}{\sqrt{1+ cos^2 \theta}}}[/tex]](images/latex/18062739a10f5c44a50269023ec9682137d94afb_0.png "[tex]z={\frac{sen}{\sqrt{1+ cos^2 \theta}}}[/tex]")
![[tex]\theta \epsilon \left [ 0, \frac{\pi}{2} \right ][/tex]](images/latex/f87ff08ddea22ede7585d6b3c0ae90730c6f3764_0.png "[tex]\theta \epsilon \left [ 0, \frac{\pi}{2} \right ][/tex]")
![[tex]x=rcos \theta[/tex]](images/latex/00a5b7d6c159b6236bdf29500eaf0718110940ef_0.png "[tex]x=rcos \theta[/tex]")
![[tex]y=r sen \theta[/tex]](images/latex/ec40015b84373dad7f60da7e74b3b91dcfb81c87_0.png "[tex]y=r sen \theta[/tex]")
![[tex]z=?[/tex]](images/latex/f03141303ccac3e87bf77445ecb3c4ebe7a388cd_0.png "[tex]z=?[/tex]")
![[tex]\left\{\begin{matrix}r^2 = 1 \\ r^2 (cos^2 \theta - sen^2 \theta )= z^2\end{matrix}\right.[/tex]](images/latex/04337487032a9987d5e469cc6756d50afec37089_0.png "[tex]\left\{\begin{matrix}r^2 = 1 \\ r^2 (cos^2 \theta - sen^2 \theta )= z^2\end{matrix}\right.[/tex]")
![[tex]\left\{\begin{matrix}r = 1 \\ z= r \sqrt{cos^2 \theta - sen^2 \theta }\end{matrix}\right.[/tex]](images/latex/3256d9ef66035750040ad9aa692363c3ea0592ed_0.png "[tex]\left\{\begin{matrix}r = 1 \\ z= r \sqrt{cos^2 \theta - sen^2 \theta }\end{matrix}\right.[/tex]")
![[tex]cos^2 \theta - sen^2 \theta=cos (2 \theta)[/tex]](images/latex/93e43d70094efbc5e14786dc7dae74cb1526d738_0.png "[tex]cos^2 \theta - sen^2 \theta=cos (2 \theta)[/tex]")
![[tex]\vec{\theta}=\left (cos \theta, sen \theta, \sqrt{cos (2 \theta)} \right )[/tex]](images/latex/e49b0fdf7b65e0c677b2e4a845f839b287d644d6_0.png "[tex]\vec{\theta}=\left (cos \theta, sen \theta, \sqrt{cos (2 \theta)} \right )[/tex]")
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