Prove that the function \(\cos \sqrt {x}\) is not periodic.
Prove the formulae: \(\arcsin (- x) = - \arcsin x\), \(\arccos (- x) = \pi - \arccos x\).
Find the locus of points whose coordinates \((x, y)\) satisfy the relation \(\sin(x + y) = 0\).
Does there exist a flat quadrilateral in which the tangents of all interior angles are equal?