MATHEMATICS ENCYCLOPEDIA

Angle is a measure of rotation of a given ray about its initial point.  The original ray is called the initial side and the final position of the ray after rotation is called the terminal side of the angle. The point of rotation is called the vertex. If the direction of rotation is anticlock, the angle is said to be positive . If the direction of rotation is clock, then the angle is negative . The measure of an angle is the amount of rotation performed to get the terminal side from the initial side. There are several units for measuring angles. Degree measure If a rotation from the initial side to terminal side is ( 1/360 )th of a revolution, the angle is said to have a measure of one degree ( 1° ). A degree is divided into 60 minutes ( 60' ). A minute is divided into 60 seconds ( 60" ). One sixtieth of a degree is called a minute, i.e. 1', and one sixtieth of a minute is called a second, i.e. 1". Thus,     1° = 60' ,  1' = 60&qu

Solution of triangles and trigonometry applications. In a triangle ABC , the angles are denoted by the capital letters A, B, C and the lengths of sides opposite to these angles are denoted by a, b, c respectively . See the figure. Some important formulae regarding the sides and angles of a triangle are given as follows: The law of  sines:  In any triangle ABC where  R  is the  radius of the circumcircle  of the triangle ABC. R is also known as the  circumradius  of the triangle. The law of  cosines:  In any triangle ABC Trigonometric ratios of half-angles in terms of the sides Let 2s = a + b + c, so that s is the semi-perimeter of triangle ABC. Then, Napier's anology: In any triangle ABC