Trigonometry is a whole branch of mathematics and does not comprise only one formula!
There are many.
No, because trigonometry is a big subject: there are many formulae.
The answer depends on what other information is available to you.
Trigonometry is basically formula's to help you find out unknown sides and angles of a triangle. Surveying is measuring land. But as not all land is equal so these formula's are used to help.
plane trigonometry spherical trigonometry
The main kinds are plane trigonometry and solid trigonometry. The latter will include trigonometry in hyper-spaces.
The general term is trigonometry. What specific formula you use depends on what other information you have.
Hipparchus is the father of trigonometry.
It is a number - in trigonometry or elsewhere.