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

• A

  $\sin \left(\frac{\theta}{2}\right)$
• B

  $\cos \left(\frac{\theta}{2}\right)$
• Correct answer
  C

  $2 \sin \left(\frac{\theta}{2}\right)$
• D

  $2 \cos \left(\frac{\theta}{2}\right)$

Solution

$\begin{aligned} & \text { In } \triangle O A M \\ & \sin \left(\frac{\theta}{2}\right)=A M \\ & \because \quad A B=2 A M \\ & \therefore \quad A B=2 \sin \left(\frac{\theta}{2}\right)\end{aligned}$

Hence, the correct answer is option: 'C'.