We are given the function \( f(2) = \sin^2(2) + \cos^2(2) \).

From trigonometry, we know the identity:
\[
\sin^2(x) + \cos^2(x) = 1
\]
This identity holds for any value of \( x \), so applying this to \( x = 2 \):

\[
\sin^2(2) + \cos^2(2) = 1
\]

Thus, \( f(2) = 1 \).

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the general form of trigonometric identities?
2. How do we derive the identity \( \sin^2(x) + \cos^2(x) = 1 \)?
3. How would \( f(x) = \sin^2(x) + \cos^2(x) \) behave for other values of \( x \)?
4. Can this identity be extended to complex numbers?
5. How does this identity relate to the Pythagorean theorem?

**Tip:** Memorizing key trigonometric identities can significantly simplify solving trigonometric problems.

Explore the solution to the function f(2) = sin^2(2) + cos^2(2) using the Pythagorean identity sin^2(x) + cos^2(x) = 1. This problem introduces fundamental trigonometric concepts and is suitable for students in Grades 9-10.

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