Question

For an acute angle \(\theta \), sin \(\theta \) + cos \(\theta \) takes the greater value when e is

• A. \(30^\circ\)
• B. \(45^\circ\)
• C. \(60^\circ\)
• D. \(90^\circ\)

Answer 1

The Correct Option is B

The correct option is (B): \(45^\circ\)
Explanation: For an acute angle \(\theta\), the expression \(\sin(\theta) + \cos(\theta)\) takes the greatest value when \(\theta = 45^\circ\).
Here's why:
- At \(\theta = 45^\circ\), both \(\sin(45^\circ) = \frac{\sqrt{2}}{2}\) and \(\cos(45^\circ) = \frac{\sqrt{2}}{2}\).
- The sum is \(\sin(45^\circ) + \cos(45^\circ) = \frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2} = \sqrt{2} \approx 1.414\), which is the maximum value for this expression.
Thus, the correct answer is Option B: \(45^\circ\).