If `y=sinx,"then at "x=pi/2,y_(2)` is equal to :

Options

A. -1
B. 1
C. 0
D. `1/2`

Answer

To solve the problem, we need to find the second derivative of the function \( y = \sin x \) at the point \( x = \frac{\pi}{2} \).

### Step-by-Step Solution:

1. **Identify the function**: We have \( y = \sin x \).

2. **First Derivative**: Differentiate \( y \) with respect to \( x \):
\[ \frac{dy}{dx} = \cos x \]

3. **Second Derivative**: Differentiate \( \frac{dy}{dx} \) with respect to \( x \) again:
\[ \frac{d^2y}{dx^2} = \frac{d}{dx}(\cos x) = -\sin x \]

4. **Evaluate the Second Derivative at \( x = \frac{\pi}{2} \)**:
\[ \frac{d^2y}{dx^2} \bigg|_{x = \frac{\pi}{2}} = -\sin\left(\frac{\pi}{2}\right) \]
Since \( \sin\left(\frac{\pi}{2}\right) = 1 \):
\[ \frac{d^2y}{dx^2} \bigg|_{x = \frac{\pi}{2}} = -1 \]

5. **Final Answer**: Therefore, \( y_{2} \) at \( x = \frac{\pi}{2} \) is:
\[ y_{2} = -1 \]