The minimum value of sin A2-√3cos A2 is attained when A is

1974 AMC 12 Problem 22

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22.

The minimum value of

\sin\frac A2-\sqrt3\cos\frac A2

is attained when

A

-180^\circ

60^\circ

120^\circ

0^\circ

none of these

Combine the sine and cosine into one shifted sine with amplitude

2

Use

\sin u-\sqrt3\cos u=2\sin(u-60^\circ)

Let

u=\frac{A}{2}.

Then

\sin u-\sqrt3\cos u

equals

2\sin(u-60^\circ).

Its minimum occurs when

u-60^\circ=270^\circ+360^\circ n,

A=660^\circ+720^\circ n

for an integer

n.

None of the first four choices has this form.

Therefore, the correct answer is E.