Trigonometry is an extremely large field (and a branch of geometry) which deals with the elucidation of the sides of a triangle based on its angles. Some common trigonometric ratios (relating to a right-angled triangle) are as follows:
sine of an angle = length of opposite side/length of hypotenuse
cosine of an angle = length of adjacent side/length of hypotenuse
tangent of an angle = length of opposite side/length of adjacent side
Of course other trigonometric ratios exist, such as cotangent, cosecant, secant of the angles. In addition, formulae such as the Sine Rule and Cosine Rule exist to allow us to elucidate the length of an unknown side based on its opposing angle and at least one other side.
As this question is relatively vague, I'm afraid that I cannot provide any further assistance in this respect.
Trigonometry is a whole branch of mathematics and does not comprise only one formula!
No, because trigonometry is a big subject: there are many formulae.
There are many.
The answer depends on what other information is available to you.
moivre's formula
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.
The general term is trigonometry. What specific formula you use depends on what other information you have.
plane trigonometry spherical trigonometry
The main kinds are plane trigonometry and solid trigonometry. The latter will include trigonometry in hyper-spaces.
Hipparchus is the father of trigonometry.
It is a number - in trigonometry or elsewhere.