Angles

Fig.(i) Fig.(ii) Fig.(iii)

Let OA and OB two half lines with common end point O. The half lines OA and OB are the sides of an angle and the point O is the vertex of the angle. An angle is an amount of rotation of a half-line (or ray) in a plane about its end point from an initial position to a terminal position.

Measurement of angle

The amount of rotation from initial side to terminal is called the measure of an angle.

Positive and Negative angles

Angles that are formed by counter clockwise (anti clockwise) rotation, such as the one shown in fig (ii) are said to be positive or to have positive measure.

Angles that are formed by a clockwise rotation, like the one in fig(iii) are said to be negative or to have negative measure.

Lines at right angles

The lines are said to be at right angles if the rotating half line (or ray) from starting from initial position to the final position describes one quarter of a circle.

Quadrants

Let X'OX and Y'OY perpendicular coplanar lines intersecting each other at O. We refer X'OX as x-axis and Y'OY as y-axis. It is clear from the adjoining figure, that these two lines divide the plane into four equal parts, each part is called a Quadrant.

The four Quadrants are:

XOY - first Quadrant

YOX' - second Quadrant

X'OY' - third Quadrant

Y'OX - fourth Quadrant

Angle in standard position

If an angle of any measure be given, one can always construct (or draw) a cartesian co-ordinate reference frame in such a way that the origin is at the vertex of the angle, and positive half of the x axis coincides with the initial side of the angle. When this has been achieved, the angle is said to be in standard position. An angle in standard position is said to be in the Quadrant in which its terminal side lies.

vi) An angle is called Quadrant angle if it is in standard position and its terminal side coincides with one of the co-ordinate axis.