Chapter 3 Class 11 Trigonometric Functions
Concept wise

We know that

Angle subtended at center of circle = 360°

And we studied that

Angle subtended at center of circle = 2π radians

So,

Radian measure = π/180  ×  Degree measure

Let’s look at some examples

Radian measure = π/180  ×  Degree measure

Radian measure = π/180  ×  30

Radian measure = π × 30/180

Radian measure = π × 1/6

Radian measure = π/180  ×  Degree measure

Radian measure = π/180  ×  45

Radian measure = π × 45/180

Radian measure = π × 1/4

Radian measure = π/180  ×  Degree measure

Radian measure = π/180  ×  60

Radian measure = π × 60/180

Radian measure = π × 1/3

Radian measure = π/180  ×  Degree measure

Radian measure = π/180  ×  90

Radian measure = π × 90/180

Radian measure = π × 1/2

Radian measure = π/180  ×  Degree measure

Radian measure = π/180  ×  0

#### 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

#### 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

#### 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

#### 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

#### 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

#### 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

Get live Maths 1-on-1 Classs - Class 6 to 12