Determine the cosine of an angle given in radians and convert it to degrees

Given an angle $ \theta = \frac{7\pi}{6} $ radians, we need to determine its cosine and convert the angle to degrees.

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First, convert the angle to degrees:\n

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$ \theta = \frac{7\pi}{6} \cdot \frac{180^\circ}{\pi} = 210^\circ $

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The angle $ 210^\circ $ lies in the third quadrant where the cosine is negative.

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Using the unit circle, we know:

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$ \cos(210^\circ) = \cos(180^\circ + 30^\circ) = -\cos(30^\circ) $

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Since $ \cos(30^\circ) = \frac{\sqrt{3}}{2} $, we have:

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$ \cos(210^\circ) = -\frac{\sqrt{3}}{2} $

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Thus, the cosine of $ \frac{7\pi}{6} $ radians is $ -\frac{\sqrt{3}}{2} $ and the angle in degrees is $ 210^\circ $.

For the angle $ heta = frac{7pi}{6} $ radians, convert it to degrees:

$ heta = frac{7pi}{6} cdot frac{180^circ}{pi} = 210^circ $

In the third quadrant, the cosine is negative:

$ cos(210^circ) = cos(180^circ + 30^circ) = -cos(30^circ) $

Since $ cos(30^circ) = frac{sqrt{3}}{2} $, we get:

$ cos(210^circ) = -frac{sqrt{3}}{2} $

The cosine of $ frac{7pi}{6} $ radians is $ -frac{sqrt{3}}{2} $ and the angle in degrees is $ 210^circ $.

For the angle $ heta = frac{7pi}{6} $ radians, convert it to degrees:

$ heta = frac{7pi}{6} cdot frac{180^circ}{pi} = 210^circ $

Since $ cos(30^circ) = frac{sqrt{3}}{2} $:

$ cos(210^circ) = -frac{sqrt{3}}{2} $

The cosine of $ frac{7pi}{6} $ radians is $ -frac{sqrt{3}}{2} $.

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