如图,点A.B.C在圆O上,∠ACB=30°,则sin∠AOB的值是 A.1/2 B.根号2/2 C.根号3/2 D.根号3/3

如图,点A.B.C在圆O上,∠ACB=30°,则sin∠AOB的值是 A.1/2 B.根号2/2 C.根号3/2 D.根号3/3
如图,点A.B.C在圆O上,∠ACB=30°,则sin∠AOB的值是 A.1/2 B.根号2/2 C.根号3/2 D.根号3/3

如图,点A.B.C在圆O上,∠ACB=30°,则sin∠AOB的值是 A.1/2 B.根号2/2 C.根号3/2 D.根号3/3
∠ACB=30°,∠ACB和∠AOB同弧,∠ACB是圆周角,∠AOB是圆心角,
∴2∠ACB=∠AOB（同弧所对的圆心角是圆周角的2倍）,
∴∠AOB=2X30°=60°.
∴sin∠AOB=sin60°=√3/2
选C.根号3/2