Problem #PRU-111925

Problems Calculus Real numbers Integer and fractional parts. Archimedean property Methods Pigeonhole principle Pigeonhole principle (angles and lengths)

Problem

On the plane coordinate axes with the same but not stated scale and the graph of the function \(y = \sin x\), \(x\) \((0; \alpha)\) are given.

How can you construct a tangent to this graph at a given point using a compass and a ruler if: a) \(\alpha \in (\pi /2; \pi)\); b) \(\alpha \in (0; \pi /2)\)?