The period of ` sin^(2)x` , is

Options

A. `2pi `
B. `pi`
C. `(pi)/(2)`
D. `4pi`

Explanation

To find the period of the function \( \sin^2 x \), we can follow these steps:

### Step 1: Use the identity for sine squared
We know from trigonometric identities that:
\[ \sin^2 x = \frac{1 - \cos(2x)}{2} \]

### Step 2: Analyze the cosine function
The function \( \cos(2x) \) is periodic. The standard period of \( \cos x \) is \( 2\pi \). However, since we have \( \cos(2x) \), we need to adjust the period based on the coefficient of \( x \).

### Step 3: Calculate the period of \( \cos(2x) \)
To find the period of \( \cos(2x) \), we use the formula for the period of \( \cos(kx) \), which is given by:
\[ \text{Period} = \frac{2\pi}{k} \]
In our case, \( k = 2 \):
\[ \text{Period of } \cos(2x) = \frac{2\pi}{2} = \pi \]

### Step 4: Determine the period of \( \sin^2 x \)
Since \( \sin^2 x \) can be expressed in terms of \( \cos(2x) \), the period of \( \sin^2 x \) is the same as the period of \( \cos(2x) \):
\[ \text{Period of } \sin^2 x = \pi \]

### Conclusion
Thus, the period of \( \sin^2 x \) is \( \pi \).