9a )\n$\\sin(\\frac{7\\pi}{6}) =$____\n# choice\na $\\frac{1}{2}$\nb $\\frac{\\sqrt{3}}{2}$\nc…

9a )\n$\\sin(\\frac{7\\pi}{6}) =$____\n# choice\na $\\frac{1}{2}$\nb $\\frac{\\sqrt{3}}{2}$\nc $-\\frac{\\sqrt{3}}{2}$\nd $-\\frac{1}{2}$

9a )\n$\\sin(\\frac{7\\pi}{6}) =$____\n# choice\na $\\frac{1}{2}$\nb $\\frac{\\sqrt{3}}{2}$\nc $-\\frac{\\sqrt{3}}{2}$\nd $-\\frac{1}{2}$

Answer

Explanation:

Step1: Expresar el ángulo

Expresar (\frac{7\pi}{6}) como (\pi+\frac{\pi}{6}). Entonces (\sin(\frac{7\pi}{6})=\sin(\pi + \frac{\pi}{6})).

Step2: Aplicar la identidad trigonométrica

Usar la identidad (\sin(A + B)=\sin A\cos B+\cos A\sin B), aquí (A = \pi) y (B=\frac{\pi}{6}). Sabemos que (\sin(\pi)=0) y (\cos(\pi)= - 1). Entonces (\sin(\pi+\frac{\pi}{6})=\sin(\pi)\cos(\frac{\pi}{6})+\cos(\pi)\sin(\frac{\pi}{6})=0\times\frac{\sqrt{3}}{2}+(-1)\times\frac{1}{2}).

Answer:

D. (-\frac{1}{2})