Short answers, pulled from the story.
Hipparchus of Nicaea is considered the father of trigonometry and he worked in the 2nd century BC. He compiled the very first trigonometric table and focused on chords to solve problems in astronomy and geometry.
Aryabhata introduced the concept of sine in the 5th century AD. His work documented in the Surya Siddhanta provided the earliest known tables of values for trigonometric ratios that were far more advanced than anything seen in the West at the time.
Nasir al-Din al-Tusi is credited with creating trigonometry as a mathematical discipline independent from astronomy. He developed spherical trigonometry into its present form and listed the six distinct cases of a right-angled triangle in spherical trigonometry.
The term trigonometry was first used by Bartholomaeus Pitiscus in his 1595 publication Trigonometria. This publication marked the formal recognition of the field as a distinct branch of mathematics.
Euler's formula states that e^(ix) = cos(x) + i*sin(x) and relates trigonometric functions to the complex exponential function. Leonhard Euler fully incorporated complex numbers into trigonometry leading to the development of this formula.
Trigonometry is used in satellite navigation systems to measure the distance to nearby stars through the technique of triangulation. It also helps determine the position of ships using sextants and marine chronometers and is used in the Global Positioning System.