| Trigonometry is a word which derives from the Greek, | | | | own separate language. |
| meaning "measure of triangles." Its origins can be | | | | Even more amazing is that this field of trigonometry |
| traced back to early Mesopotamia where sailors and | | | | can be learned by understanding some simple |
| navigators invented this discipline to help determine | | | | relationships, and I guess the most rudimentary ones |
| position and location. To think an act so simple as the | | | | are the sine, cosine, and tangent of a given angle. In |
| measurement of triangles and the study of | | | | the simplest of language, the sine is the ratio, or |
| relationships between its angles and sides could | | | | quotient, formed by the length of the opposite side to |
| harbinger the development of a mathematical discipline | | | | the length of the hypotenuse. The hypotenuse is the |
| which in turn would find itself involved in such diverse | | | | longest side of any right triangle, and is the side directly |
| fields as astronomy, navigation, music theory, acoustics, | | | | opposite the right angle-bigger angle opens up to a |
| optics, electronics, economics, number theory, | | | | bigger, or longer side. Thus if we look at a standard |
| pharmacy, chemistry, geodesy, cartography, | | | | right triangle with side lengths of 3, 4, and 5 (which one |
| crystallography, architecture, oceanography, | | | | must be the hypotenuse?), then the sine of the angle |
| engineering, game theory, ultrasound, cryptography, | | | | formed by the hypotenuse and the shorter leg is 4/5 |
| meteorology, seismography, medical imaging (i.e. CAT | | | | or 0.8 (opposite the shorter leg is the longer leg). |
| scans), phonetics, statistics, and biology, to name a | | | | Similarly, the sine formed by the hypotenuse and the |
| few-then you have thought rightly. | | | | longer leg is 3/5 or 0.6. That's all there is to it. The |
| If the list of fields above astounds you, then you are | | | | ratios for the cosine and tangent-which we shall |
| not alone. Many people go through life without learning | | | | explore in another article-can be found using the |
| even the most superficial mysteries of mathematics. If | | | | SOHCAHTOA mnemonic. (See my article "Why |
| any language is universal, mathematics is the ultimate | | | | Study Math? Trigonometry and SOHCAHTOA") |
| lingua franca. Mathematics is indeed the language of | | | | Once we understand these ratios, we can then delve |
| the universe-the language that is understood and | | | | into the wonderful world of trigonometry and all its |
| applicable in star systems within galaxies so remote | | | | glorious applications in fields like the ones mentioned in |
| that the only way to visit them is within the constructs | | | | the first paragraph. Gee, is it any wonder that |
| of our minds. If this fact does not amaze you then look | | | | mathematics is so fascinating? So remember. The |
| at a more mundane comparison: in the country of India, | | | | next time someone asks you what your sign is, don't |
| language diversity is so enormous that even different | | | | say Aries, or Gemini, or Leo; but rather say, |
| villages only miles away from each other have their | | | | trigonometry. |