University of South Carolina High School Math Contest/1993 Exam/Problem 10
Problem
Arcsin(1/3) + Arccos(1/3) + Arctan(1/3) + Arccot(1/3) =
![$\mathrm{(A) \ }\pi \qquad \mathrm{(B) \ }\pi/2 \qquad \mathrm{(C) \ }\pi/3 \qquad \mathrm{(D) \ }2\pi/3 \qquad \mathrm{(E) \ }3/\pi/4$](http://latex.artofproblemsolving.com/9/7/b/97b0fa52186af1028b00c9f5a690827a039634be.png)
Solution
If we construct right triangles for each pair of arguments ( and
), we see that the sum of the angles is
.