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) =

$\mathrm{(A) \ }\pi \qquad \mathrm{(B) \ }\pi/2 \qquad \mathrm{(C) \ }\pi/3 \qquad \mathrm{(D) \ }2\pi/3 \qquad \mathrm{(E) \ }3/\pi/4$

Solution

If we construct right triangles for each pair of arguments ( $\arcsin, \arccos$ and $\arctan, \arccot$ (Error compiling LaTeX. Unknown error_msg)), we see that the sum of the angles is $90^\circ+90^\circ=\pi$ .

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

Problem

Solution