Questions: sin(5π/6)

Transcript text: $\sin \left(\frac{5 \pi}{6}\right)$

Solution

Step 1: Identify the angle in radians

The given angle is $ \frac{5\pi}{6} $, which is in radians.

Step 2: Determine the reference angle

The angle $ \frac{5\pi}{6} $ lies in the second quadrant. The reference angle is calculated as: \[ \pi - \frac{5\pi}{6} = \frac{\pi}{6} \]

Step 3: Evaluate the sine of the reference angle

The sine of $ \frac{\pi}{6} $ is: \[ \sin\left(\frac{\pi}{6}\right) = \frac{1}{2} \]

Step 4: Determine the sign of the sine function in the second quadrant

In the second quadrant, the sine function is positive. Therefore: \[ \sin\left(\frac{5\pi}{6}\right) = \frac{1}{2} \]

$\boxed{\frac{1}{2}}$

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