If a circle subtends at the center an angle whose radian measure is 2π and its degree measure is 360°. That is
2π = 360° and π = 180°
The above relation enables us to express an radian measures in terms of degree measure and a degree measure in terms of radian measure.Using the approximate value of π as 22/7, we have
1 radian = 180°/π
1 radian = 180°/π
1 radian = 180°/3.14
1 radian = 57° 19' approximately
Also, 1° = π/180° radian = 0.01745 radians approximately
The relation between degree measures and radian measure of some common angles are given in the following list.
π/2 = 90°
π/3 = 60°
π/6 = 30°
π/4 = 45°
π = 180°
3π/2 = 270°
2π = 360°
To convert from radian to degree, we have to use the formula given below.
Degree measure = (180°/π) x Radian measure
Let us look into some examples to know that how to convert the degree measure from radian.
Example 1 :
Convert 6 radians to degree measure.
Solution :
To convert 6 radians to degree, we need to use the formula.
Degree measure = (180°/π) x Radian measure
6 radian = 6 x (180°/π) radians
= (180° x 6) / π
= 1080°/π
Substitute 3.14 for π and simplify.
≈ 343.95°
To convert from radian to degree, we have to use the formula given below.
Radian measure = (π/180°) x degree measure
Example 2 :
Convert 40° 30' to radian measure.
Solution :
To convert 40° 30' to radians, we need to use the formula.
Radian measure = (π/180°) x degree measure
40° 30' :
= 40° + 30'
= 40° + (30/60)°
= 40° + 0.5°
= 40.5°
= 40.5°
= 40.5° x π/180° radians
Substitute 3.14 for π and simplify.
≈ 0.7065 radians
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