Question

The distance between $A(\cos \theta ,\sin \theta )$ and $B(-\sin \theta ,\cos \theta )$ is

• A. 1
• B. $2+2\sin \theta$
• C. $1+\sin \theta$
• D. $\sqrt{2}$

Answer 1

Answer: (D)

$\sqrt{2}$

Given $A(\cos \theta ,\sin \theta )$ and $B(-\sin \theta ,\cos \theta )$

Distance between $AB=\sqrt{(\cos \theta +\sin \theta {)}^2+(\sin \theta -\cos \theta {)}^2}=\sqrt{{\cos }^2\theta +{\sin }^2\theta +2\sin \theta \cos \theta +{\cos }^2\theta +{\sin }^2\theta -2\sin \theta \cos \theta }=\sqrt{1+1}=\sqrt{2}$