Trigonometry

Trigonometry is a branch of mathematics that solves problems relating to plane and spherical triangles. Its principles are based on the fixed proportions of sides for a particular angle in a right-angled triangle, the simplest of which are known as the sine, cosine, and tangent (so-called trigonometric ratios). Trigonometry is of practical importance in navigation, surveying, and simple harmonic motion in physics.

Using trigonometry, it is possible to calculate the lengths of the sides and the sizes of the angles of a right-angled triangle as long as one angle and the length of one side are known, or the lengths of two sides. The longest side, which is always opposite to the right angle, is called the hypotenuse . The other sides are named depending their position relating to the angle that is to be found or used: the side opposite this angle is always termed opposite and that adjacent is the adjacent .

The methods of elementary trigonometry can be used to solve problems in three dimensions by considering triangles in different planes that have a side in common. This may also involve the use of a dropping perpendicular, that is the envisaging of an imaginary line from a point above the base that will fall vertically to the base. Spherical triangles can be solved using the trigonometric functions, though the formulae are not the same as those employed for plane triangles.

Trigonometry arose out of the study of astronomy, and was originated by the Greek astronomer Hipparchus. It was also known to early Hindu and Arab mathematicians. Ptolemy the Alexandrian astrologer, greatly extended the subject and German astronomer Regiomontanus made it a science independent of astronomy much later on, when he began compiling trigonometric tables in 1467.

The above material is quoted from the Hutchinson Family Encyclopedia , available at http://ebooks.whsmithonline.co.uk/ .