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

  1. Chapter 3 Class 11 Trigonometric Functions
  2. Concept wise
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Transcript

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.

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