Trigonometry
RADIANS
RADIANS
This chapter will cover the measure of angles in terms of radians and degrees.
EO 1.4
STATE the definition of a radian.
Radian Measure
The size of an angle is usually measured in degrees. However, in some applications the size of
an angle is measured in radians. A radian is defined in terms of the length of an arc subtended
by an angle at the center of a circle. An angle whose size is one radian subtends an arc whose
length equals the radius of the circle. Figure 4 shows BAC whose size is one radian. The
length of arc BC equals the radius r of the circle. The size of an angle, in radians, equals the
length of the arc it subtends divided by the radius.
(4-8)
Figure 4 Radian Angle
Radians
Length of Arc
Radius
One radian equals approximately 57.3 degrees. There are
exactly 2p radians in a complete revolution.
Thus 2p
radians equals 360 degrees: p radians equals 180 degrees.
Although the radian is defined in terms of the length of an
arc, it can be used to measure any angle. Radian measure
and degree measure can be converted directly. The size of
an angle in degrees is changed to radians by multiplying
by
. The size of an angle in radians is changed to
p
180
degrees by multiplying by
.
180
p
Example:
Change 68.6° to radians.
068.6°
p
180
(68.6)p
180
1.20 radians
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