Question

O soluție a ecuatiei “radical din 3•sinx+cosx=0’’din intervalul[0, 2pi] este?

Answer 1

[tex]\text{Iti prezint o metoda interesanta de rezolvare:}\\ \sqrt 3\cdot \sin x+\cos x=0\\ \\ ctg\ \dfrac{\pi}{6}\cdot \sin x+\cos x=0\\ \dfrac{\cos \frac{\pi}{6}}{\sin \frac{\pi}{6}}\sin x+\cos x=0|\cdot \sin \dfrac{\pi}{6}\\ \\ \cos \dfrac{\pi}{6}\cdot \sin x+\cos x\cdot \sin \dfrac{\pi}{6}=0\\ \sin \left(x+\dfrac{\pi}{6}\right)=0\\ x+\dfrac{\pi}{6}=k\ccdot \pi,k\in \mathbb{Z}\\ x=k\cdot \pi -\dfrac{\pi}{6}\\ \text{Dandu-i lui k valoarea 1 se obtine:}\\ x=\pi-\dfrac{\pi}{6}=\dfrac{5\cdot \pi}{6} [/tex]