Ecuatii trigonometrice

Ecuatia cosx=1 are soluțiile 

• $\pm\frac{\pi}{2}+k\pi,k\in Z$

• $\pm\pi k,k\in Z$

• $2k\pi,k\in Z$

• $\pm\frac{\pi}{4}+2k\pi,k\in Z$

Ecuatia sinx= - 2 are solutiile

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

• n-are solutii

• $\pm2k\pi,k\in Z$

• $\frac{\pi}{2}+2k\pi,k\in Z$

DVA al ecuaței  tgx=2 este:

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

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

• $R\ne\left\{k\pi,k\in Z\right\}$

• $\left\{\pi k,k\in Z\right\}$

 $2\sin^2x+5\sin x=3\ este\ ecuatie:$  

• Trigonometrica fundamentala

• Trigonometrica omogena

• Trigonometrica reductibila la ecuatii algebrica

• Nu este ecuatie trigonometrica

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

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

•  $R$  

•  $\left\{k\pi,k\in Z\right\}$  

• 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 

•  $\left\{\pm k\pi,k\in Z\right\}$  

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

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

•  $\left\{\pm2k\pi,k\in Z\right\}$  

Ecuatia de forma   $\cos^2x+5\cos x\sin x-\sin^2x=0\$  

este ecuație:

• Trigonometrica fundamentala

• Trigonometrica omogena

• Trifonometrica reductibila la ecuatii algebrice

• Nu este ecuatie trigonometrica

Rezolvă ecuația $\cos^2x-2\sin x\cos x=1\$  apoi 

bifează răspunsul corect

•  $\left\{\pm k\pi,k\in Z\right\}$  

•  $\left\{\pm\frac{\pi}{3}+2k\pi,k\in Z\right\}\cup\left\{n\pi,n\in Z\right\}$  

•  $\left\{\frac{\pi}{2}+2k\pi,k\in Z\right\}\cup\left\{\frac{\pi}{3}+n\pi,n\in Z\right\}$  

• N-are solutii