Trigonometry

Trigonometry is the branch of mathematics that deals with the relationships between the sides and angles of triangles. The word "trigonometry" comes from the Greek words for "triangle" and "measurement." In simple terms, trigonometry is all about triangles!

The basic concepts of trigonometry can be understood by considering the most basic type of triangle, the right triangle. A right triangle is a triangle in which one of the angles is a right angle (90 degrees). The other two angles are acute angles (less than 90 degrees).

The sides of a right triangle are usually labeled with the letters a, b, and c, like this:

The side opposite the right angle is called the hypotenuse. The other two sides are called the legs.

The most basic trigonometric ratios are the ratios of the lengths of the sides of a right triangle. These ratios are always the same, no matter how big or small the triangle is. They are:

• The ratio of the length of the hypotenuse to the length of the leg closest to the right angle is called the cosine (abbreviated cos).
• The ratio of the length of the leg furthest from the right angle to the length of the leg closest to the right angle is called the sine (abbreviated sin).
• The ratio of the length of the hypotenuse to the length of the leg furthest from the right angle is called the tangent (abbreviated tan).

To find the values of these ratios, we need to know the lengths of the sides of the triangle. But sometimes, all we know are the angles of the triangle. This is where trigonometry comes in!