Geometry is the study of shapes and the science of finding the measurements and angles of those shapes. For the most part, this study is rather straightforward. Most shapes have very clear definitions with very few variations of the rules governing them. However, triangles stand out among geometric shapes. There are several types of triangles and even more specific ways to measure the dimensions. In fact, triangles are so complex, there’s a specific set of mathematical tools for them. These tools are called trigonometry.

Trigonometry comes from the Latin root words of triganon, meaning triangle, and metron, meaning measure. The very term trigonometry means to measure triangles. This set of mathematic functions isn’t reserved only for solving problems on a work sheet. Originally, trigonometry as we know was used for navigation on the seas, where no landmarks were visible. This should indicate just how complex this study is, but it can also indicate just how powerful the functions of trigonometry can be.

The Functions of Trigonometry

Depending on the person asked, there may be 1, 3, 6, or even twelve total trig functions.

The minimalist answer is that there is only on true function, sine. This is because the other functions can be considered derivatives of Sine. Even cosine can be derived by using Sine. The minimalist answer may be the most simple and straightforward way to remember the rules of trig.

The calculator answer is that there are three functions. This is because there are three buttons to choose from, which are cosecant, secant, and cotangent. However, these buttons can be combined to use the other functions.

The textbook answer is that there are six answers. They are sine, cosine, tangent, cosecant, secant, and cotangent. Although, these functions can be expressed in more familiar terms, reducing the effective answer to three.

Historically speaking, there are actually twelve functions. In addition to the six listed above, they are versine, haversine, coversine, hacoversine, exsecant, and excosecant. When trig was used to navigate on the seas, these functions served a specific purpose and were used regularly by navigators who were specially trained in there use. Since navigation is mostly computerized these days, those functions tend to stay in the past where they belong.

Where to Use Trig Functions

Going by the text book answer, there are six functions that need to be explained so they can be used properly. These are sine, cosine, tangent, cosecant, secant, and cotangent. Each has a specific purpose and can even be used to derive some of the more historical functions.

Sine is equal to the ratio of the side opposite a given angle in a right triangle to the hypotenuse.

Cosine is equal to the ratio of the side adjacent to an acute angle in a right-angled triangle to the hypotenuse.


Cosecant is the ratio of the hypotenuse in a right triangle to the side opposite an acute angle.

Secant is the ratio of the hypotenuse to the shorter side adjacent to an acute angle in a right triangle.

Cotangent is the ratio of the side, other than the hypotenuse, adjacent to a particular acute angle to the side opposite the angle in a right triangle.

Definitions of these functions can be helpful, but the only way to truly understand them is to practice them. Only by using these functions in real problems can they be mastered. It’s all about practice, practice, practice.