Il seno di x è una funzione trigonometrica di fondamentale importanza nell'analisi matematica. In questa pagina potete trovare il grafico e le proprietà della funzione seno.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBYXX5epByqr7th0ry6lNcCsiVTkInB244EbHCE3RtGCwxuE2DRlpR0K12lMlCEwqxzvifWnaNz6_2_6oBvOT69VIUDGsAgAWOaa2geFRIBFZIfipFGD9uvnn76vx06WFof7X7IJ23gbU/s1600-rw/function-seno.gif)
Sviluppo di Taylor:
GRAFICO DELLA FUNZIONE SENO
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBYXX5epByqr7th0ry6lNcCsiVTkInB244EbHCE3RtGCwxuE2DRlpR0K12lMlCEwqxzvifWnaNz6_2_6oBvOT69VIUDGsAgAWOaa2geFRIBFZIfipFGD9uvnn76vx06WFof7X7IJ23gbU/s1600-rw/function-seno.gif)
PROPRIETA' DELLA FUNZIONE SENO
Dominio: ![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEje-rFdJtrwbG9hX9P3Hj17RUO_K6mOPY-MjVi9mJ2UmUWjERpzmh0O35K8YqJHtbFwontNNtvoTF6rxNdUuY_ii0JHR2r-Zgzv4n4RsqrnJUaPL8h1vuW_K6KDL-q2nsWLfBAVtDxv9w4/s1600-rw/dominio.gif)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEje-rFdJtrwbG9hX9P3Hj17RUO_K6mOPY-MjVi9mJ2UmUWjERpzmh0O35K8YqJHtbFwontNNtvoTF6rxNdUuY_ii0JHR2r-Zgzv4n4RsqrnJUaPL8h1vuW_K6KDL-q2nsWLfBAVtDxv9w4/s1600-rw/dominio.gif)
Periodicità: ![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKDYCKlPEdvRLlPpUmz3fc9zgtWkD5AYaogb72L5wE3qiaWN-dRQMpTn52Ae66o7LkOi8k4wIL9iC3i4_QdTJisS6SSeRUR5FUywAA49n6QUHti9bqQQoFBAmQnLdt9v5TTK6bZeb-RG8/s1600-rw/2-p-greco.gif)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKDYCKlPEdvRLlPpUmz3fc9zgtWkD5AYaogb72L5wE3qiaWN-dRQMpTn52Ae66o7LkOi8k4wIL9iC3i4_QdTJisS6SSeRUR5FUywAA49n6QUHti9bqQQoFBAmQnLdt9v5TTK6bZeb-RG8/s1600-rw/2-p-greco.gif)
Monotonia (intervalli di crescenza/descrescenza): crescente su
, decrescente su tutta la restante parte di dominio.
![\left[0,\frac{\pi}{2}\right)\cup\left[\frac{3}{2}\pi,2\pi\right)](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8nrzo5hEAyyFvrXBUwNUVjFReSroGglnMNwwAvvbVcqxJtWLiElk3Do86hpyB63Z48-xuPjaWh5p0NF1PBg2orNCL1NJH1k0IRLc-P8QznTY0uPOkEsHn_oyzbopM_g0WeUjb19hzf78/s1600-rw/monotonia-intervalli.gif)
Concava (cioè con cavità verso il basso) su
, convessa sulla parte restante di dominio.
![\left[0,\pi\right]](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhe-B2lRForzDxUzP9MzHXAyf2fn6t1csu7Z6t5l4fyhUYvyo3naDwbgW2zobosGA70jm0xnQYTgpeVHLaZCI7kKAx80THElC8GmnSGhtD9NBv0mKFvdHHf-MuoiNVckOKp1GmUdxuFaQc/s1600-rw/0-p-greco.gif)
Continua su tutto
, derivabile su tutto ![\mathbb{R}](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEigUPbphjniIgMUspoJS58UKtF48XxMOtaCJ5NAjzsq0SdzeYSWS3BElGYyEwF-PhWkn2PuRLwTsSit02IrYun1Eja9YPpLayKby9tnZO6DLuMrKRSVFDxC2tPhM0yYKwWHMFv3iyUL6-Y/s1600-rw/R-numeri-reali.gif)
![\mathbb{R}](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEigUPbphjniIgMUspoJS58UKtF48XxMOtaCJ5NAjzsq0SdzeYSWS3BElGYyEwF-PhWkn2PuRLwTsSit02IrYun1Eja9YPpLayKby9tnZO6DLuMrKRSVFDxC2tPhM0yYKwWHMFv3iyUL6-Y/s1600-rw/R-numeri-reali.gif)
![\mathbb{R}](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEigUPbphjniIgMUspoJS58UKtF48XxMOtaCJ5NAjzsq0SdzeYSWS3BElGYyEwF-PhWkn2PuRLwTsSit02IrYun1Eja9YPpLayKby9tnZO6DLuMrKRSVFDxC2tPhM0yYKwWHMFv3iyUL6-Y/s1600-rw/R-numeri-reali.gif)
Derivata: ![\frac{d}{dx}\sin{(x)}=\cos{(x)}](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYwZcbwqS1hqO-AiBjcXaczA-lN0aODRM00gaUaaWT-njIeMlW_6HzR928L9NZ8XHK8eQgT6XQ5fUWMOuLa8sPSiSp-FuR4UlCs7_tL1cGuQytI-7OQ6ebsW8598kYNWIIz4G0mBGGs6A/s1600-rw/derivata.gif)
![\frac{d}{dx}\sin{(x)}=\cos{(x)}](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYwZcbwqS1hqO-AiBjcXaczA-lN0aODRM00gaUaaWT-njIeMlW_6HzR928L9NZ8XHK8eQgT6XQ5fUWMOuLa8sPSiSp-FuR4UlCs7_tL1cGuQytI-7OQ6ebsW8598kYNWIIz4G0mBGGs6A/s1600-rw/derivata.gif)
Integrale: ![\int{\sin{(x)}dx}=-\cos{(x)}+c](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjP3TYMi5EVlK0R-irFw4A0ORzdcLvgjU0p1RYI8MymWXExkYtYVWzs5wbR2PyEZ0yPaFdTnBNm4FJlqEOcowDyIGir6s6S0LkmKoGuUgm2YcK5OkfmuwcKjH55NAfyGiZPtV6EBtXmHZ8/s1600-rw/integrale.gif)
![\int{\sin{(x)}dx}=-\cos{(x)}+c](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjP3TYMi5EVlK0R-irFw4A0ORzdcLvgjU0p1RYI8MymWXExkYtYVWzs5wbR2PyEZ0yPaFdTnBNm4FJlqEOcowDyIGir6s6S0LkmKoGuUgm2YcK5OkfmuwcKjH55NAfyGiZPtV6EBtXmHZ8/s1600-rw/integrale.gif)
Limite notevole associato: ![\lim_{x\to 0}\frac{\sin{(x)}}{x}=1](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiK8AwnV7MQLV5JcAg4ieZzGXhRw3IQIHSdzo4aJZyXJeQFtm6p2tRoJ6SPl_dbgUUfw9z_7xYdoxThMKYhyphenhyphenp_BFVZPsgqhLF0mOrkwvboZk4QzGqvLk48w5UCm3inLnJIY0tf_iCNY57U/s1600-rw/limite-notevole-associato.gif)
![\lim_{x\to 0}\frac{\sin{(x)}}{x}=1](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiK8AwnV7MQLV5JcAg4ieZzGXhRw3IQIHSdzo4aJZyXJeQFtm6p2tRoJ6SPl_dbgUUfw9z_7xYdoxThMKYhyphenhyphenp_BFVZPsgqhLF0mOrkwvboZk4QzGqvLk48w5UCm3inLnJIY0tf_iCNY57U/s1600-rw/limite-notevole-associato.gif)
Limiti agli estremi del dominio: NON ESISTONO, poichè la funzione seno è una funzione limitata e compresa tra -1 ed 1 e quindi non tende all'infinito. (si, si è una funzione pigra, non vuole muoversi dal letto :D :D)
Sviluppo di Taylor:
![\sin(x)=x-\frac{x^3}{6}+\frac{x^5}{120}-\frac{x^7}{5040}+...+\frac{(-1)^n x^{2n+1}}{(2n+1)!}+o(x^{2n+1})](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_jPLzQMjIGqty5djJkl9L86yCsKosTUQZ4Dmp9PNFuNsArE6hm7Bpkzm7vHrnFIE6_ki7VzJeozxi1N0_Uz4YJQtXJYlgS4dK7KGQfmlqT6bsVI8vZYhgci0Jtd-cVQrgtr-kxQjxqXU/s1600-rw/sviluppo-taylor.gif)
Autore: Pierfrancesco Di Vanni