Question

The greatest and least values of \( \left( \sin(x) \right)^2 + \left( \cos(x) \right)^2 \) are respectively

• A. \( \frac{\pi}{2} \) and 0
• B. \( \frac{\pi}{4} \) and \( -\frac{\pi}{2} \)
• C. \( \frac{5\pi}{2} \) and \( \frac{\pi}{8} \)
• D. \( \frac{\pi}{2} \) and \( -\frac{\pi}{4} \)

Hint:

Use trigonometric identities to simplify and find the extreme values of expressions involving sine and cosine.

Answer 1

The Correct Option is C

Step 1: Use the trigonometric identity.
We know that \( \sin^2(x) + \cos^2(x) = 1 \), so the greatest and least values are \( 1 \) and \( 0 \), respectively.
Step 2: Conclusion.
The greatest value is 1 and the least value is 0. Final Answer: \[ \boxed{1 \text{ and } 0} \]