Trigonometry is the study of triangles and angles and their relationship. The greatest example of a practical use of such knowledge can be seen in the great Pyramids of Egypt. From very early times, surveyors, navigators and astronmers have used triangles to measure distances that could not be measured directly. Ancient Egyptian papri dating from at least 1600 B.C., show considerable evidence of pratical problems solved by triangle measurement.

The characteristics of similar triangles, originally formulated by Euclid, are the buiding blocoks of trigonometry. Euclid's theorems state if two angles of one triangle have the same measure as two angles of another triangle then the two triangles are similar. Also, in similar triangles, angle measure and ratios of corresponding sides are preserved. Since all right triangles contain a a 90° (degrees) angle, all right triangles that contain another angle of equal measure must be similar. Therefore the ratio of the corresponding sides of these triangles must be equal in value. These relationships lead to the trigonometric ratios. Lower case Greek letters are usually used to name angle measures. It doesn't matter which letter is used, but two that are used quite often are alpha (α) and theta (θ).

There are six trigonometric ratios sine, cosine, tangent, cotangent, secant, and cosecant.

For example: sin q = ½