What is the length of the chord of a unit circle which subtends an angle at the centre ?

Options

A. `sin(theta/2)`
B. `cos((theta)/(2))`
C. `2sin((theta)/(2))`
D. `2cos((theta)/(2))`

Answer

To find the length of the chord of a unit circle that subtends an angle at the center, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We have a unit circle (a circle with a radius of 1) and we need to find the length of the chord that subtends an angle θ at the center of the circle.

2. **Identify the Radius**: For a unit circle, the radius \( R \) is equal to 1.

3. **Use the Chord Length Formula**: The length \( L \) of a chord that subtends an angle \( \theta \) at the center of a circle is given by the formula:
\[ L = 2R \sin\left(\frac{\theta}{2}\right) \]

4. **Substitute the Radius**: Since we are dealing with a unit circle, we substitute \( R = 1 \) into the formula:
\[ L = 2 \cdot 1 \cdot \sin\left(\frac{\theta}{2}\right) \]

5. **Simplify the Expression**: This simplifies to:
\[ L = 2 \sin\left(\frac{\theta}{2}\right) \]

6. **Final Result**: Therefore, the length of the chord is:
\[ L = 2 \sin\left(\frac{\theta}{2}\right) \]