Find the exact value of $\cos 120^\circ$:

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**Solution:**

1. Recall the identity:  $\cos 	heta = \sin (90^\circ - 	heta)$.

2. Express $120^\circ$ as $90^\circ + 30^\circ$.

3. Using the cosine addition formula or unit circle knowledge, in the second quadrant (where $120^\circ$ lies), cosine values are negative.

4. Calculate:
   $$\cos 120^\circ = \cos (90^\circ + 30^\circ) = -\sin 30^\circ$$

5. Since $\sin 30^\circ = 0.5$, we get:
   $$\cos 120^\circ = -0.5$$

**Answer:** $-0.5$

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