A recall of basic results

Until now, trigonometric ratios have been defined only for the acute angles of a right triangle, and the identities proved were valid only in that restricted setting. But many of the real distances and heights we actually want to measure — the distance between planets, the height of a mountain, the distance from the Earth to the Sun, the height of a tall building, or the speed of a supersonic jet — cannot always be captured by an acute angle sitting inside a right triangle.

The goal of this chapter is therefore to broaden the very definition of a trigonometric function so that it applies to any real number, not merely to angles between $0^\circ$ and $90^\circ$. This broader definition is what makes trigonometry usable throughout the rest of mathematics, and especially in calculus. …