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

Problem

$\arcsin\left(\frac{1}{3}\right) + \arccos\left(\frac{1}{3}\right) + \arctan\left(\frac13\right) + \arccot\left(\frac13\right) =$ (Error compiling LaTeX. Unknown error_msg)

Solution

If we construct right triangles for each pair of arguments ( in one triangle and $\arctan, \arccot$ (Error compiling LaTeX. Unknown error_msg) in another), we see that the sum of the angles is .

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