Trigonometry

Trigonometry is about studying triangles and, in particular, the relation of their angles to their edges. The ratio of two of the three edges (sides) of a triangle gives information about a particular angle, and to such a pair of sides, we give it a certain name and call it a function. The beauty of trigonometry and mathematics in general is that these functions, which are born inside a triangle, make (abstract) sense in any other situation where triangles are not present and operate as independent mathematical objects. Hence, functions such as the tangent, cosine, and sine are found across most fields of mathematics, physics, and engineering without any reference to the triangle.

Let's look at the most fundamental trigonometric functions and their usage.

Basic Trigonometric Functions

We will start by defining a right-angled triangle (or simply a right triangle), triangle ABC. One of its angles (the angle BCA in the following diagram) is a right angle, that...