1974 AHSME Problem 22

The minimum of \sin\frac{A}{2}-\sqrt{3}\cos\frac{A}{2} is attained when A is

\mathrm{(A)\ } -180^\circ \qquad \mathrm{(B) \ }60^\circ \qquad \mathrm{(C) \ } 120^\circ \qquad \mathrm{(D) \ } 0^\circ \qquad \mathrm{(E) \ }\text{none of these}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.