University of South Carolina High School Math Contest/1993 Exam/Problem 10

Problem

$\mathrm{(A) \ }\pi \qquad \mathrm{(B) \ }\pi/2 \qquad \mathrm{(C) \ }\pi/3 \qquad \mathrm{(D) \ }2\pi/3 \qquad \mathrm{(E) \ ...$

If we construct right triangles for each pair of arguments ( $\arcsin, \arccos$ in one triangle and $\arctan, \text{arccot}$ in another), we see that the sum of the angles is $90^\circ+90^\circ=\pi$ .