Question

Sa se rezolve ecuatiile:

a)sinx= -1 b)cosx= -$\frac{ \sqrt{3} }{2}$.
Cum se afla x? Ma intereseaza modul de lucru.

Answer 1

Salut,

Soluţia corectă şi completă se află mai jos:

$sinx=-1\Rightarrow x=(-1)^k\cdot arcsin(-1)+k\pi=\\\\=(-1)^{k+1}\cdot arcsin 1+k\pi=(-1)^{k+1}\cdot\dfrac{\pi}2+k\pi;\\\\cosx=-\dfrac{\sqrt3}2\Rightarrow x=\pm arccos\left(-\dfrac{\sqrt3}{2}\right)+2k\pi=\\\\=\pm\left[\pi-arccos\left(\dfrac{\sqrt3}{2}\right)\right]+2k\pi=\\\\=\pm\left(\pi-\dfrac{\pi}6\right)+2k\pi=\pm\dfrac{5\pi}6+2k\pi.$

Green eyes.