TRIGONOMETRIC FUNCTIONS Arya Bhatt ( - ) Fig . Vertex MATHEMATICS 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 anticlockwise, the angle is said to be positive and if the direction of rotation is clockwise, then the angle is negative (Fig .
). 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. The definition of an angle suggests a unit, viz.
one complete revolution from the position of the initial side as indicated in Fig . . This is often convenient for large angles. For example, we can say that a rapidly spinning wheel is making an angle of say revolution per second.
We shall describe two other units of measurement of an angle which are most commonly used, viz. degree measure and radian measure. . .
Degree measure If a rotation from the initial side to terminal side is th of a revolution, the angle is said to have a measure of one degree , written as °. A degree is divided into minutes, and a minute is divided into seconds . One sixtieth of a degree is called a minute , written as ′ , and one sixtieth of a minute is called a second , written as ″ . Thus, ° = ′, ′ = ″ Some of the angles whose measures are °, °, °, °, – °, – ° are shown in Fig .
. Fig . Fig . TRIGONOMETRIC FUNCTIONS .
. Radian measure There is another unit for measurement of an angle, called the radian measure. Angle subtended at the centre by an arc of length unit in a unit circle (circle of radius unit) is said to have a measure of radian. In the Fig .
(i) to (iv), OA is the initial side and OB is the terminal side.