$Find the cosine values on the unit circle for specific angles$

Let’s find the cosine values for angles 120°, 210°, and 330° on the unit circle.

First, convert the angles into radians:

$120° = \frac{2\pi}{3}$

$210° = \frac{7\pi}{6}$

$330° = \frac{11\pi}{6}$

Next, we use the unit circle to find the cosine values for each angle:

For $\frac{2\pi}{3}$, the cosine value is:

$\cos \frac{2\pi}{3} = -\frac{1}{2}$

For $\frac{7\pi}{6}$, the cosine value is:

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

For $\frac{11\pi}{6}$, the cosine value is:

$\cos \frac{11\pi}{6} = \frac{\sqrt{3}}{2}$

To find the cosine values for the angles 135°, 225°, and 315° on the unit circle, we first convert them to radians:

$135° = frac{3pi}{4}$

$225° = frac{5pi}{4}$

$315° = frac{7pi}{4}$

Using the unit circle, we obtain:

For $frac{3pi}{4}$:

$cos frac{3pi}{4} = -frac{sqrt{2}}{2}$

For $frac{5pi}{4}$:

$cos frac{5pi}{4} = -frac{sqrt{2}}{2}$

For $frac{7pi}{4}$:

$cos frac{7pi}{4} = frac{sqrt{2}}{2}$

Convert the following angles 150°, 240°, and 360° to radians:

$150° = frac{5pi}{6}$

$240° = frac{4pi}{3}$

$360° = 2pi$

On the unit circle:

$cos frac{5pi}{6} = -frac{sqrt{3}}{2}$

$cos frac{4pi}{3} = -frac{1}{2}$

$cos 2pi = 1$

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