Calculate the exact value of $sinleft(frac{7pi}{6}
ight)$ using the unit circle

To determine the exact value of $\sin\left(\frac{7\pi}{6}\right)$ using the unit circle, first note that $\frac{7\pi}{6}$ is in the third quadrant.

In the third quadrant, the sine function is negative.

Now, find the reference angle for $\frac{7\pi}{6}$:

$ 7\pi / 6 – \pi = \pi / 6 $

The reference angle is $\pi / 6$, whose sine value is $\frac{1}{2}$.

Since sine is negative in the third quadrant:

$ \sin \left( \frac{7\pi}{6} \right) = -\frac{1}{2} $

To find the value of $sinleft( frac{7pi}{6}
ight)$:

First, recognize that $frac{7pi}{6}$ is in the third quadrant.

The reference angle is:

$ frac{7pi}{6} – pi = frac{pi}{6} $

The sine of $frac{pi}{6}$ is $frac{1}{2}$, and sine is negative in the third quadrant:

$ sin left( frac{7pi}{6}
ight) = -frac{1}{2} $

For $sin left( frac{7pi}{6}
ight)$:

Reference angle:

$ frac{7pi}{6} – pi = frac{pi}{6} $

Thus:

$ sin left( frac{7pi}{6}
ight) = -frac{1}{2} $

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