Functia+tangenta

 **Functia tangenta**  **Definitie:** Tangenta unui unghi α notata tgα este raportul dintre sinusul unghiului α si cosinusul acestuia.    **PROPRIETATI :**  1. Functia tangenta este o functie periodica de perioada kπ tg(α+kπ) =tgα pentru oricare α apartine lui R din care scadem 2. Functia tangenta este o functie impara tg (-x)=-tg(x) <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: justify;"> <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 120%;">3. Intersectia graficului cu axa ox se face in punctele de abscisa x= kπ(k є Z). <span style="background-color: #ffffff; color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 120%;"> Intersectia cu axa oy se face in punctul 0(0,0).

<span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 120%;"> 4. Monotonie : daca x 1 ,x 2 є ( -π/2, π/2) ,x 1 <x 2 , atunci x 1 - x 2 є (-π,0). Din tgx 1 -tgx 2 = sin(x 1 -x 2 ) / (cosx 1 cosx 2 ), sin(x 1 -x 2 )<0, cosx 1 >0 , cosx 2 >0, rezulta tgx 1 <tgx 2. Functia tg este deci strict crescatoare pe orice interval din domeniul ei de definitie de forma (kπ-π/2, π/2+kπ) k є Z.

<span style="background-color: #ffffff; color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 120%;">5. Functia tg are valori pozitive pe intervalul (kπ, π/2 + kπ) si valori negative pe intarvalul (π/2+kπ,π+kπ).

<span style="background-color: #ffffff; color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 120%;">6. Functia tg:R\{(2k+1)π/2}→R nu este bijectiva deci nu este inversabila. In schimb f: (-π/2,π/2)→R, f(x)=tg(x) este bijectiva si este inversabila. <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 120%;">7. Functia este concava pe intervale de forma (kπ-π/2, kπ) k є Z si este convexa pe intervale de forma (0+kπ, π/2+kπ) k є Z


 * > <span style="background-color: #ffffff; color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 120%; text-align: center;">Cadranul ||> <span style="background-color: #ffffff; color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 120%; text-align: center;">I  ||> <span style="background-color: #ffffff; color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 120%; text-align: center;">II  ||> <span style="background-color: #ffffff; color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 120%; text-align: center;">III  ||> <span style="background-color: #ffffff; color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 120%; text-align: center;">IV  ||
 * <span style="background-color: #ffffff; color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 120%; text-align: center;">Functia tangenta || <span style="background-color: #ffffff; color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 120%; text-align: center;">+  || <span style="background-color: #ffffff; color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 120%; text-align: center;">-  || <span style="background-color: #ffffff; color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 120%; text-align: center;">+  || <span style="background-color: #ffffff; color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 120%; text-align: center;">-  ||

<span style="background-color: #ffffff; color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 120%;">4. Functia tangenta este strict crescatoare pe intervale de forma

<span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="background-color: #ffffff; color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 120%; text-align: justify;">5. Graficul functiei tangenta <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: justify;"><span style="background-color: #ffffff; color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 120%;">

<span style="background-color: #ffffff; color: #000000; display: block; font-family: Arial,Helvetica,sans-serif; font-size: 120%; text-align: justify;">**Tabelul de valori al functiei tg** <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 120%;">**Managed by Farcas Cosmina & Bobernac Alexandru**
 * <span style="background-color: #ffffff; color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 120%; vertical-align: baseline;">x || <span style="background-color: #ffffff; color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 120%; vertical-align: baseline;">-π/2  || <span style="background-color: #ffffff; color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 120%; vertical-align: baseline;">-π/3  || <span style="background-color: #ffffff; color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 120%; vertical-align: baseline;">-π/4  || <span style="background-color: #ffffff; color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 120%; vertical-align: baseline;">-π/6  || <span style="background-color: #ffffff; color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 120%; vertical-align: baseline;">0  || <span style="background-color: #ffffff; color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 120%; vertical-align: baseline;">π/6  || <span style="background-color: #ffffff; color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 120%; vertical-align: baseline;">π/4  || <span style="background-color: #ffffff; color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 120%; vertical-align: baseline;">π/3  || <span style="background-color: #ffffff; color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 120%; vertical-align: baseline;">π/2  ||
 * <span style="background-color: #ffffff; color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 120%; vertical-align: baseline;">tg x || <span style="background-color: #ffffff; color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 120%; vertical-align: baseline;">| -∞  || <span style="background-color: #ffffff; color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 120%; vertical-align: baseline;">-√3  || <span style="background-color: #ffffff; color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 120%; vertical-align: baseline;">-1  || <span style="background-color: #ffffff; color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 120%; vertical-align: baseline;">-√3/3  || <span style="background-color: #ffffff; color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 120%; vertical-align: baseline;">0  || <span style="background-color: #ffffff; color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 120%; vertical-align: baseline;">√3/3  || <span style="background-color: #ffffff; color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 120%; vertical-align: baseline;">1  || <span style="background-color: #ffffff; color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 120%; vertical-align: baseline;">√3  || <span style="background-color: #ffffff; color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 120%; vertical-align: baseline;">+∞ |  ||