To express $\cos(60^\circ + \theta)$ as a function of $\theta$, we can use the cosine angle addition formula:

$\cos(a + b) = \cos a \cdot \cos b - \sin a \cdot \sin b$

For $a = 60^\circ$ and $b = \theta$:

1. $\cos(60^\circ) = \frac{1}{2}$
2. $\sin(60^\circ) = \frac{\sqrt{3}}{2}$

Substituting these values into the formula gives:

$\cos(60^\circ + \theta) = \cos(60^\circ) \cdot \cos(\theta) - \sin(60^\circ) \cdot \sin(\theta)$

Thus:

$\cos(60^\circ + \theta) = \frac{1}{2} \cdot \cos(\theta) - \frac{\sqrt{3}}{2} \cdot \sin(\theta)$

So, the expression simplifies to:

$\cos(60^\circ + \theta) = \frac{1}{2} \cos(\theta) - \frac{\sqrt{3}}{2} \sin(\theta)$

Summary:

$\cos(60^\circ + \theta) = \frac{1}{2} \cos(\theta) - \frac{\sqrt{3}}{2} \sin(\theta)$

Would you like any further details or explanations? Here are some related questions you might consider:

1. What is the sine addition formula?
2. How does changing the angle affect the cosine function?
3. Can you derive the sine of the angle using the sine addition formula?
4. What are some applications of angle addition formulas in trigonometry?
5. How can we visualize the function $\cos(60^\circ + \theta)$?

Tip: Always remember to refer back to the unit circle for values of sine and cosine at special angles.