ANSWER
The first choice is correct.
EXPLANATION
We want to use the unit circle to determine the sine, cosine and tangent of the angle,
[tex] \alpha = - \frac{3\pi}{6} [/tex]
This simplifies to
[tex]\alpha = - \frac{\pi}{2} [/tex]
This is a quadrantal angle. This angle intercepts the unit circle at, (0,-1).
We know that on the unit circle, the x-coordinate is given by;
[tex]x = \cos( \alpha ) [/tex]
Hence
[tex] \cos( \alpha ) = 0[/tex]
and the y-coordinate is given by;
[tex] y = \sin( \alpha ) [/tex]
This implies that
[tex] \sin( \alpha ) = - 1[/tex]
The tangent is
[tex] \tan( \alpha ) = \frac{ \sin( \alpha ) }{ \cos( \alpha ) } = \frac{ - 1}{0} = undefined[/tex]
The correct choice is A.
