Find the exact values of $cos frac{7pi}{6}$ and $sin frac{7pi}{6}$ using the unit circle.

To find the exact values of $\cos \frac{7\pi}{6}$ and $\sin \frac{7\pi}{6}$, we start by locating the angle on the unit circle. The angle $\frac{7\pi}{6}$ is in the third quadrant.

We know that $\frac{7\pi}{6} = \pi + \frac{\pi}{6}$. This means the reference angle is $\frac{\pi}{6}$.

In the third quadrant, both the cosine and sine values are negative. The reference angle $\frac{\pi}{6}$ has known values of $\sin \frac{\pi}{6} = \frac{1}{2}$ and $\cos \frac{\pi}{6} = \frac{\sqrt{3}}{2}$.

Thus:

$\cos \frac{7\pi}{6} = -\cos \frac{\pi}{6} = -\frac{\sqrt{3}}{2}$

$\sin \frac{7\pi}{6} = -\sin \frac{\pi}{6} = -\frac{1}{2}$

To determine the values of $cos frac{7pi}{6}$ and $sin frac{7pi}{6}$, we first recognize that $frac{7pi}{6}$ is an angle in the third quadrant.

The reference angle for $frac{7pi}{6}$ is $pi – frac{7pi}{6} = frac{pi}{6}$.

In the third quadrant, both sine and cosine are negative. From the unit circle, $sin frac{pi}{6} = frac{1}{2}$ and $cos frac{pi}{6} = frac{sqrt{3}}{2}$.

Therefore:

$cos frac{7pi}{6} = -frac{sqrt{3}}{2}$

$sin frac{7pi}{6} = -frac{1}{2}$

To find the values of $cos frac{7pi}{6}$ and $sin frac{7pi}{6}$, note that $frac{7pi}{6}$ is in the third quadrant. The reference angle is $frac{pi}{6}$.

In the third quadrant, cosine and sine are negative. Thus:

$cos frac{7pi}{6} = -frac{sqrt{3}}{2}$

$sin frac{7pi}{6} = -frac{1}{2}$

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