Question

find the exact value of the trigonometric function.
\\( \sin \theta \\)
\\( \frac{\sqrt{3}}{2} \\)
\\( \frac{1}{2} \\)
1
-1

Explanation:

Step1: Recall the unit - circle definition of sine

For an angle \(\theta\) in standard position, \(\sin\theta=y\) where \((x,y)\) is the point on the unit - circle corresponding to \(\theta\).

Step2: Find the \(y\) - coordinate for \(\theta=\frac{\pi}{2}\)

On the unit - circle, when \(\theta = \frac{\pi}{2}\), the point is \((0,1)\).

Answer:

\(1\)