In the xy-plane above, O is the center of the circle, and the measure of `angle`AOB is `(pi)/(a)` radians. What is the value of a ?

Explanation

The correct answer is 6. By the distance formula, the length of readius OA is `sqrt((sqrt(3))^(2)+1^(2))=sqrt(3+1)=2.` Thus, `sin(angle AOB)=(1)/(2)`. Therefore, the measure of `angle AOB` is `30^(@)`, which is equal to `30((pi)/(180))=(pi)/(6)` radians. Hence, the value of a is 6.