To solve \( \cos^2(0) \):

1. We start by evaluating \( \cos(0) \).
   \[
   \cos(0) = 1
   \]

2. Next, we square this result:
   \[
   \cos^2(0) = (1)^2 = 1
   \]

Therefore, \( \cos^2(0) = 1 \).

Would you like a more detailed explanation or have any questions?

Here are some related questions to deepen understanding:

1. What is \( \cos^2(\pi) \)?
2. How does \( \sin^2(x) + \cos^2(x) = 1 \) apply to angles like \(0\) or \(\pi/2\)?
3. What does \( \cos^2(x) \) represent graphically?
4. How would \( \cos^2(x) \) differ if \( x = 45^\circ \)?
5. How can we calculate \( \cos^2(x) \) using trigonometric identities?

**Tip:** When squaring trigonometric functions like \( \cos(x) \), remember that the result is always non-negative.

Discover how to evaluate cos^2(0) with a step-by-step solution. This problem explores essential trigonometric concepts and the Pythagorean Identity theorem, making it suitable for students in Grades 9-12.

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