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

9c )\n\n$\\sin(\\frac{7\\pi}{6}) =$____\n\n# choice\n\na $\\frac{\\sqrt{3}}{2}$\n\nb $-\\frac{1}{2}$\n\nc $\\frac{1}{5}$

9c )\n\n$\\sin(\\frac{7\\pi}{6}) =$____\n\n# choice\n\na $\\frac{\\sqrt{3}}{2}$\n\nb $-\\frac{1}{2}$\n\nc $\\frac{1}{5}$

Answer

Explanation:

Step1: Expresar el ángulo como una suma

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: [ \begin{align*} \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}\ &=-\frac{1}{2} \end{align*} ]

Answer:

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