Question

find the exact value of sin(π/6). sin(π/6)=□ (type a simplified fraction. type an exact answer, using radicals as needed. rationalize the denominator.)

Explanation:

Step1: Recall special - angle values

The sine of $\frac{\pi}{6}$ is a well - known value in trigonometry. In a right - triangle with angles $\frac{\pi}{6}$, $\frac{\pi}{3}$, and $\frac{\pi}{2}$, if the hypotenuse is of length $2$, the side opposite the angle $\frac{\pi}{6}$ has length $1$.
By the definition of sine function $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, for $\theta = \frac{\pi}{6}$, we have $\sin\frac{\pi}{6}=\frac{1}{2}$.

Answer:

$\frac{1}{2}$