Answer
$s=\dfrac{7\pi}{4}$
Work Step by Step
Use the inverse tangent function of a calculator in radian mode to obtain:
$s =\tan^{-1}{(-1)}=-\frac{1}{4}\pi$
Since the angle must be within the interval $[\frac{3\pi}{2}, 2\pi]$, find the positive coterminal angle of $-\frac{1}{4}\pi$ in Quadrant IV. This angle can be found by adding $2\pi$ to the given angle to obtain:
$-\frac{1}{4}\pi + 2\pi = -\frac{1}{4}\pi+\frac{98}{4}\pi=\frac{7}{4}\pi$
Thus, $-\frac{1}{4}\pi$ and $\frac{7}{4}\pi$ are coterminal angles and therefore have the same tangent value.
Thus,
$s=\dfrac{7\pi}{4}$
