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?

Observe that $$\tan(\pi/2-\beta)=\frac{\sin(\pi/2-\beta)}{\cos(\pi/2-\beta)}=\frac{\cos\beta}{\sin\beta}=\frac{1}{\tan\beta}$$
