Does there exist a function \(f (x)\) defined for all real numbers such that \(f(\sin x) + f (\cos x) = \sin x\)?
Suppose that in each issue of our journal in the “Quantum” problem book there are five mathematics problems. We denote by \(f (x, y)\) the number of the first of the problems of the \(x\)-th issue for the \(y\)-th year. Write a general formula for \(f (x, y)\), where \(1 \geq x \geq 12\) and \(1970 \geq y \geq 1989\). Solve the equation \(f (x, y) = y\). For example, \(f (6, 1970) = 26\). Since \(1989\), the number of tasks has become less predictable. For example, in recent years, half the issues have 5 tasks, and in other issues there are 10. Even the number of magazine issues has changed, no longer being 12 but now 6.