equazioni trigonometriche

cos(x)=1, x=?

• $\pm\frac{\pi}{2}+k\pi,k\in Z$

• $\pm\pi k,k\in Z$

• $2k\pi,k\in Z$

• $\pm\frac{\pi}{4}+2k\pi,k\in Z$

 $\sin\left(x\right)=-2,\ x=...$  

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

• impossibile

• $\pm2k\pi,k\in Z$

• $\frac{\pi}{2}+2k\pi,k\in Z$

 $2\sin\left(x\right)=0,\ x=...?$  

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

•  $R$  

•  $\left\{k\pi,k\in Z\right\}$  

• Nu are solutii

  $2\sin\left(2x-3\right)=\sqrt{2},\ x=...?$  

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

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

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

• impossibile

 $\cos^2x+2\cos x+1=0,\ x=...?$  

•  $\left\{\pm k\pi,k\in Z\right\}$  

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

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

•  $\left\{\pm2k\pi,k\in Z\right\}$  

L'equazione $\cos^2x+5\cos x\sin x-\sin^2x=0\$  è

• un'equazione trigonometrica fondamentale

• un'equazione trigonometrica omogenea

• un'equazione trigonometrica riconducibile a un'equazione algebrica

• non è un'equazione trigonometrica 

 $\cos^2x-2\sin x\cos x=1,\ x=...?$  

•  $\left\{\pm k\pi,k\in Z\right\}$  

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

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

• impossibile

Solve on the domain [0, 2π)
4sin²x = 3

• π/6, 11π/6
• π/3, 2π/3
• π/6, 5π/6, 7π/6, 11π/6
• π/3, 2π/3, 4π/3, 5π/3

 $\sin\left(2x\right)=0,\ x=...?$  

• x= $\pi$ k

• $\frac{\pi}{2}k$

• 2 $\pi$ k

• $\frac{\pi}{2}+\pi k$

 $\cos\left(\frac{x}{2}\right)=0,\ x=...?$ 

• 4 $\pi$  k

• 2 $\pi$  k

•  $\pi$  +2 $\pi$  k

•  $\pi$  +4 $\pi$  k