evaluate. write your answer in simplified, rationalized form. do not round. \n$\\sin\\left(\\frac{\\pi}{3}\\r…

Explanation:

Step1: Recall the value of sine for special angles

We know that for the unit - circle, the sine of an angle $\theta$ in the first quadrant is given by the $y$ - coordinate of the point on the unit - circle corresponding to the angle $\theta$. For $\theta=\frac{\pi}{3}$ (60 degrees), the coordinates of the point on the unit - circle are $(\cos\frac{\pi}{3},\sin\frac{\pi}{3})=(\frac{1}{2},\frac{\sqrt{3}}{2})$.

Answer:

$\frac{\sqrt{3}}{2}$