The word Trigonometry comes from the Greek words 'trigonon' and 'metria' meaning triangle and measure respectively. Trigonon itself consists of two words 'Tri' meaning three and 'gonia' meaning angle. You can clearly see that 'Tri' is nothing but the Sanskrit root Tri and 'gonia' is derived from the Sanskrit word Kona (angle). In the Sanskritic vernaculars of India, trigonometry is called Trikonamiti (Tri-Kona-Miti).
The importance of Trigonometry lies in the fact that any computational problem in geometry can be reduced to solution of triangles. Because of this, Trigonometry finds extensive applications in plane geometry, solid geometry, natural sciences and the engineering. The aim of trigonometry is to find solutions of triangles, that is, given certain quantities of the triangle, we can find the unknown quantities of the triangle. Where as, Plane Trigonometry deals with ordinary triangles, Spherical Trigonometry deals with spherical triangles.
Trigonometric functions are relations that connect the angles of an arbitrary triangle with its sides. The value of a trigonometric function can be computed from a given angle and conversely. Trigonometric function is so called because it varies with the angle to which it corresponds. The various trigonometric functions are interrelated. These relationships are used to reduce and simplify computations. The part of trigonometry that deals with such relations is Analytical Trigonometry or Goniometry (the measurement of angles). In Greek, gonia means angle, derived from the Sanskrit word Kona as I have stated at the beginning.