Question

The maximum value of \(3\cos\theta + 4\sin\theta\) is

• A. -5
• B. 5
• C. 25
• D. None of these

Hint:

\(a\cos\theta + b\sin\theta\) lies between \(-\sqrt{a^2 + b^2}\) and \(\sqrt{a^2 + b^2}\).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Maximum of \(a\cos\theta + b\sin\theta = \sqrt{a^2 + b^2}\).
Step 2: Detailed Explanation:
Maximum value = \(\sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5\)
Step 3: Final Answer:
5.