Ecuatii trigonometrice

Ecuatia cosx=1 are soluțiile 

•  $\left\{\pm\frac{\pi}{2}+k\pi,k\in Z\right\}$ 

•  $\left\{\pm\pi k,k\in Z\right\}$ 

•  $\left\{2k\pi,k\in Z\right\}$ 

•  $\left\{\pm\frac{\pi}{4}+2k\pi,k\in Z\right\}$ 

Ecuatia sinx= - 2 are solutiile

• $\left\{\left(-1\right)^k\arcsin\left(-2\right)\pm k\pi,k\in Z\right\}$

• n-are solutii

• $\left\{\pm2k\pi,k\in Z\right\}$

• $\left\{\frac{\pi}{2}+2k\pi,k\in Z\right\}$

 $Ecuatia\ 2\sin x=0\ are\ solutiile$  

•  $\left\{\pm\frac{\pi}{2}+k\pi,k\in Z\right\}$  

•  $R$  

•  $\left\{k\pi,k\in Z\right\}$  

• Nu are solutii

 $Ecuația\ \operatorname{ctg}x=4\ are\ soluțiile:$  

•  $\left\{4k\pi,k\in Z\right\}$  

•  $\left\{\operatorname{arcctg}4\ +k\pi,k\in Z\right\}$  

•  $\left\{ar\operatorname{ctg}4\ +k\pi,k\in Z\right\}$  

• Nu are solutii

Rezolvă ecuația  $2\sin\left(2x-3\right)=\sqrt{2},apoi\ bifeaza$  

•  $\left\{\frac{\pi}{4}+k\pi,k\in Z\right\}$  

•  $\left\{\left(-1\right)^k\ \frac{\pi}{8}+\frac{3}{2}+\frac{k\pi}{2},k\in Z\right\}$  

•  $\left\{\left(-1\right)^k\ \frac{\pi}{3}+\frac{k\pi}{2},k\in Z\right\}$  

• N-are solutii

Rezolvă $\cos^2x+2\cos x+1=0\$ 

apoi bifează răspunsul corect 

•  $\left\{\pm k\pi,k\in Z\right\}$  

•  $\left\{\pm\pi+2k\pi,k\in Z\right\}$  

•  $\left\{\left(-1\right)^k\pi+k\pi,k\in Z\right\}$  

•  $\left\{\pm2k\pi,k\in Z\right\}$  

 $Ecuatia\ \sin x=0\ are\ solutiile$  

•  $\left\{\pm\frac{\pi}{2}+k\pi,k\in Z\right\}$  

•  $R$  

•  $\left\{k\pi,k\in Z\right\}$  

• Nu are solutii

 $Ecuatia\ \operatorname{ctg}x=4\ are\ solutiile$  

•  $\left\{4k\pi,k\in Z\right\}$  

•  $\left\{\operatorname{arcctg}4\ +k\pi,k\in Z\right\}$  

•  $\left\{ar\operatorname{ctg}4\ +k\pi,k\in Z\right\}$  

• Nu are solutii

soluția ecuației cos $\frac{x}{2}$  =0 este 

•  $\left\{\pm4k\pi,\ k\in Z\right\}$ 

•  $\left\{\pm2k\pi,\ k\in Z\right\}$  

•  $\left\{\pm\pi\ +2k\pi,\ k\in Z\right\}$  

•  $\left\{\pi\ +2k\pi,\ k\in Z\right\}$  

Soluția ecuației sin2x=0 este

• $\left\{\left(-1\right)^k\pi+k\pi,k\in Z\right\}$

• $\left\{\frac{k\pi}{2},\ k\in Z\right\}$

• 2

• $\frac{\pi}{2}$