Question

Решить уравнение: sin(π-x)=cos(π/3)

Answer 1

$\sin(\pi -x)=\cos\dfrac{\pi}{3}$

$\sin(\pi -x)=\dfrac{1}{2}$

$\pi -x=(-1)^k\dfrac{\pi}{6} +\pi k$

$x=\pi-(-1)^k\dfrac{\pi}{6} +\pi k$

$x=\pi+(-1)^{k+1}\dfrac{\pi}{6} +\pi k,\ k\in\mathbb{Z}$

Ответ: $\pi+(-1)^{k+1}\dfrac{\pi}{6} +\pi k,\ k\in\mathbb{Z}$