Answer
$sin(\frac{3\pi}{2}) = -1$
$cos(\frac{3\pi}{2}) = 0$
$tan(\frac{3\pi}{2}) = undefined$
$csc(\frac{3\pi}{2}) = -1$
$sec(\frac{3\pi}{2}) = undefined$
$cot(\frac{3\pi}{2}) = 0$
\begin{bmatrix}
t & sin \space t & cos \space t & tan \space t & csc \space t & sec \space t & cot \space t \\
0 & 0 & 1 & 0 & undef. & 1 & undef. \\
\frac {\pi} 2 & 1 & 0& undef. & 1 & undef. & 0\\
\pi & 0 & -1 & 0 & undef. & -1 & undef.\\
\frac{3\pi}{2} & -1 & 0 & undef. & -1 & undef. & 0
\end{bmatrix}
Work Step by Step
1. Find a Reference Number.
$t^- = \frac{3\pi}2 - \pi = \frac{\pi} 2$
2. See Table 1 (Page 410), it contains all the values for the trigonometric functions when $t = \pi/2$.
$sin(\frac{\pi}{2}) = 1$
$cos(\frac{\pi}{2}) = 0$
$tan(\frac{\pi}{2}) = undefined$
$csc(\frac{\pi}{2}) = 1$
$sec(\frac{\pi}{2}) = undefined$
$cot(\frac{\pi}{2}) = 0$
3. Since $3\pi/2$ is in Quadrant III, sin($3\pi/2$) and csc($3\pi/2$) are negative.
$sin(\frac{3\pi}{2}) = -1$
$cos(\frac{3\pi}{2}) = 0$
$tan(\frac{3\pi}{2}) = undefined$
$csc(\frac{3\pi}{2}) = -1$
$sec(\frac{3\pi}{2}) = undefined$
$cot(\frac{3\pi}{2}) = 0$
4. Completing the Table:
\begin{bmatrix}
t & sin \space t & cos \space t & tan \space t & csc \space t & sec \space t & cot \space t \\
0 & 0 & 1 & 0 & undef. & 1 & undef. \\
\frac {\pi} 2 & 1 & 0& undef. & 1 & undef. & 0\\
\pi & 0 & -1 & 0 & undef. & -1 & undef.\\
\frac{3\pi}{2} & -1 & 0 & undef. & -1 & undef. & 0
\end{bmatrix}