ADVERTISEMENT

Section 6.1 Angle Measure

An angle AOB consists of two rays R

and R

with a common vertex O (see the Figures

1

2

below). We often interpret an angle as a rotation of the ray R

onto R

. In this case, R

is

1

2

1

called the initial side, and R

is called the terminal side of the angle. If the rotation is

2

counterclockwise, the angle is considered positive, and if the rotation is clockwise, the angle

is considered negative.

Angle Measure

The measure of an angle is the amount of rotation about the vertex required to move R

1

onto R

. Intuitively, this is how much the angle “opens.” One unit of measurement for angles

2

1

is the degree. An angle of measure 1 degree is formed by rotating the initial side

of a

360

complete revolution. In calculus and other branches of mathematics, a more natural method

of measuring angles is used — radian measure. The amount an angle opens is measured along

the arc of a circle of radius 1 with its center at the vertex of the angle.

The circumference of the circle of radius 1 is 2π and so a complete revolution has measure 2π

rad, a straight angle has measure π rad, and a right angle has measure π/2 rad. An angle that

is subtended by an arc of length 2 along the unit circle has radian measure 2 (see the Figures

below).

◦

Since a complete revolution measured in degrees is 360

and measured in radians is 2π rad, we

get the following simple relationship between these two methods of angle measurement.

1

ADVERTISEMENT

0 votes

Parent category: Education