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

Answer: (B)

$45^\circ$

Answer 2

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: $45^\circ$.