What is a Degree Measure?
One degree is one 360th part of a full circle. To get a more clear idea we define degree measure as follows:
A central angle that is subtended by an arc equal in length to 1/360 of the circle's circumference, is said to have a measure of one degree, denoted 1°.
That is; for a circle with circumference C units, central angle of θ degrees subtended by an arc of s units, this relationship can be expressed by the following proportion:
The degree is further divided in to 60 minutes.
For even finer measurements the minute is divided again into 60 seconds; however this last measure is so small, it only used where angles are subtended over extreme distances such as astronomical measurements, and measuring latitude and longitude.
What is a Radian Measure
The radian is the standard unit of angular measure. It describes the plane angle subtended by a circular arc as the length of the arc divided by the radius of the arc.
One radian is the angle made at the center of a circle by an arc whose length is equal to the radius of the circle. The radian is a fixed size no matter what the size of the circle is.
- A full angle is 2Π radians, so there are 360° per 2Π radians, equal to 180° / Π.
- A right angle is Π / 2 radians and a straight angle is Π radians.
Relation between Degree and Radian
A circle subtends at the centre an angle whose radian measure is 2Π and its degree measure is 360°,
Radian to Degree
Also, 1 radian = 180° / Π
Or, Radian Measure = x Degree Measure
Degree to Radian
On the basis of above discussion, we now solve the following questions:
1. Convert 40° 20’ into radian measure.
We know, 180° = Π radian
40° 20’ = 40 degree = x radian = radian.
2. Convert 6 radians into degree measure.
We know, Π radian = 180°
6 radians = x 6 degree = degree
343 degree = 343° + minute [As 1° = 60’]
343° + 38’ + minute [As 1’ = 60’’]
343° + 38’ + 10.9’’’
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