Chapter 1.7, Problem 42ES

Writing Let $\theta ={\tan }^{-1}\left(-3/4\right)$ and explain why the triangle in the accompanying figure may be used to evaluate $\sin \theta$ and $\cos \theta$ . More generally, suppose that $q$ denotes a rational number and that $\theta ={\tan }^{-1}q$ or that $\theta ={\sin }^{-1}q$ . Find right triangles, with at least two sides labelled by integers, that may be used to evaluate $\sin \theta$ and $\cos \theta$ .