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We know that
Angle subtended at center of circle = 360°
And we studied that
Angle subtended at center of circle = 2π radians
So,
360° = 2π radians
360°/2 = π radians
180° = π radians
To convert degrees and radians,
Radian measure = π/180 × Degree measure
Let’s look at some examples
Convert 30° into radians
Radian measure = π/180 × Degree measure
Radian measure = π/180 × 30
Radian measure = π × 30/180
Radian measure = π × 1/6
Radian measure = π/6
∴ 30° = π/6 radians
Convert 45° into radians
Radian measure = π/180 × Degree measure
Radian measure = π/180 × 45
Radian measure = π × 45/180
Radian measure = π × 1/4
Radian measure = π/4
∴ 45° = π/4 radians
Convert 60° into radians
Radian measure = π/180 × Degree measure
Radian measure = π/180 × 60
Radian measure = π × 60/180
Radian measure = π × 1/3
Radian measure = π/3
∴ 60° = π/3 radians
Convert 90° into radians
Radian measure = π/180 × Degree measure
Radian measure = π/180 × 90
Radian measure = π × 90/180
Radian measure = π × 1/2
Radian measure = π/2
∴ 90° = π/2 radians
Convert 0° into radians
Radian measure = π/180 × Degree measure
Radian measure = π/180 × 0
Radian measure = 0
∴ 30° = 0 radians
Convert π radians into degree
Radian measure = π/180 × Degree measure
π = π/180 × Degree measure
π × 180/π = Degree measure
180 = Degree measure
Degree measure = 180
∴ π radian = 180°
Convert π /6 radians into degree
Radian measure = π/180 × Degree measure
π/6 = π/180 × Degree measure
π/6 × 180/π = Degree measure
π/π × 180/6 = Degree measure
1 × 30 = Degree measure
30 = Degree measure
Degree measure = 30
∴ π/6 radian = 30°
Convert π /3 radians into degree
Radian measure = π/180 × Degree measure
π/3 = π/180 × Degree measure
π/3 × 180/π = Degree measure
π/π × 180/3 = Degree measure
1 × 60 = Degree measure
60 = Degree measure
Degree measure = 60
∴ π/3 radian = 60°
Convert π /4 radians into degree
Radian measure = π/180 × Degree measure
π/4 = π/180 × Degree measure
π/4 × 180/π = Degree measure
π/π × 180/4 = Degree measure
1 × 45 = Degree measure
45 = Degree measure
Degree measure = 45
∴ π/4 radian = 45°
Convert π /2 radians into degree
Radian measure = π/180 × Degree measure
π/2 = π/180 × Degree measure
π/2 × 180/π = Degree measure
π/π × 180/2 = Degree measure
1 × 90 = Degree measure
90 = Degree measure
Degree measure = 90
∴ π/2 radian = 90°
Convert 1 radians into degree
Radian measure = π/180 × Degree measure
1 = π/180 × Degree measure
180/π = Degree measure
Degree measure = 180/π
∴ 1 radian = 180/π °
In some cases, we have to divide and convert degrees into minutes. Check this question
