Answer
(a) $\sin{(-\frac{3\pi}{2})}=1$
(b) $\cos{(-\frac{3\pi}{2})}=0$
(c) $\tan{(-\frac{3\pi}{2})}=\dfrac{1}{0}, \text{ undefined}$
Work Step by Step
Using Figure 13 on page 579 of this book, the angle $-\frac{3\pi}{2}$, which is $\frac{3\pi}{2}$ units clockwise from the positive x-axis, intersects the unit circle at the point $(0, 1)$.
RECALL:
In a unit circle,
(1) $\cos{s} = x$
(2) $\sin{s} = y$
(3) $\tan{s} = \dfrac{y}{x}$
Thus, use the definitions above to obtain:
(a) $\sin{(-\frac{3\pi}{2})}=1$
(b) $\cos{(-\frac{3\pi}{2})}=0$
(c) $\tan{(-\frac{3\pi}{2})}=\dfrac{1}{0}, \text{ undefined}$
