Triangle trigonometry

The functions $\sin$, $\cos$, $\tan$ were not born to play with the trigonometric circle: they were born from the need to solve triangles, that is, to determine all their elements — sides and angles — starting from some given data. In this chapter we develop “classical” trigonometry, the one that was at the heart of mathematics teaching from the Middle Ages until the nineteenth century, with the two fundamental theorems for general triangles: the cosine rule (or Carnot’s theorem) and the sine rule. We shall also see the trigonometric formula for the area, Heron’s formula as a corollary and the chord theorem, which links chords and angles in the circumscribed circle.

Sections

• Trigonometry in right-angled triangles
• The cosine rule (or Carnot’s theorem)
• The sine rule
• Area of a triangle
• The chord theorem

Exercises

• All the worked exercises of the chapter