Short answers, pulled from the story.
Trigonometry is a branch of mathematics concerned with the relationships between the angles and side lengths of triangles. Its trigonometric functions relate the angles of a right triangle to ratios of its side lengths.
Trigonometry emerged in the Hellenistic world during the 3rd century BC, growing out of applications of geometry to astronomical studies. The Greeks focused on calculating chords, while mathematicians in India created the earliest-known tables of values for ratios such as sine.
The Persian polymath Nasir al-Din al-Tusi has been described as the creator of trigonometry as a mathematical discipline in its own right. He was the first to treat it as independent from astronomy and developed spherical trigonometry into its present form.
Bartholomaeus Pitiscus was the first to use the word, publishing his Trigonometria in 1595.
The six trigonometric functions are sine, cosine, and tangent, along with their reciprocals the cosecant, secant, and cotangent. Sine is the ratio of the opposite side to the hypotenuse, cosine the ratio of the adjacent leg to the hypotenuse, and tangent the ratio of the opposite leg to the adjacent leg.
Trigonometry is applied in astronomy, navigation, surveying, and geodesy, and continues through the Global Positioning System and artificial intelligence for autonomous vehicles. It also underpins the study of periodic functions for sound and light waves, medical imaging such as CT scans and ultrasound, and fields ranging from acoustics and optics to computer graphics and game development.