Question

question 17
find the exact value of the trigonometric function.
\\( \sin \left( \frac{\pi}{6} \
ight) = \\)
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Explanation:

Step1: Recall the unit - circle values

On the unit circle, for an angle \(\theta=\frac{\pi}{6}\) (or \(30^{\circ}\)), the coordinates of the point on the unit circle are \((\cos\frac{\pi}{6},\sin\frac{\pi}{6})\).
The unit - circle definition of sine is \(y\) - coordinate of the point \((x,y)\) on the unit circle corresponding to the angle \(\theta\).
For \(\theta = \frac{\pi}{6}\), the point on the unit circle is \((\frac{\sqrt{3}}{2},\frac{1}{2})\).

Answer:

\(\frac{1}{2}\)