Why does $\tan\left(\frac{\pi}{2} - \beta\right) = \frac{t}{s}$ imply that $\tan\beta = \frac{s}{t}$? I have been preparing for the SAT on KhanAcademy. For one of the trigonometry problems, the following conversion is made:
$$\tan\left(\frac{\pi}{2} − \beta\right)= \frac{t}{s}$$
$$\tan(\beta) = \frac{s}{t}$$
There is no explanation for how this change works. Can anyone explain?

$$\tan (90^\circ - x) \equiv \cot x = \frac{1}{\tan x}$$
