Question

evaluate. write your answer in simplified, rationalized form. do not round. sin(π/3) =

Explanation:

Step1: Recall the unit - circle value

The sine of an angle in the unit circle. For the angle \(\frac{\pi}{3}\) (60 degrees), from the properties of a 30 - 60 - 90 triangle. In a 30 - 60 - 90 triangle with hypotenuse \(c = 2\), the side opposite the 60 - degree angle \(a=\sqrt{3}\) and the side opposite the 30 - degree angle \(b = 1\).
The formula for \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\).
For \(\theta=\frac{\pi}{3}\), \(\sin(\frac{\pi}{3})=\frac{\sqrt{3}}{2}\)

Answer:

\(\frac{\sqrt{3}}{2}\)