Degree and Radian Measure Formula

In mathematics, the radian is the standard unit of angular measure. An angle’s measurement in radians is numerically equal to the length of a corresponding arc of a unit circle. The relationship or the connection between the arc length and radius of a circle defines the radian of a circle. Degree and radian formula used to convert, degree to radian or radian to degree.

\[\LARGE Radian=\frac{Arc\;Length}{Radius\;Length}\]

\[\LARGE Radian=\frac{Degree\times \pi}{180}\]

Here are few Degree Measures and their corresponding Radian Measures – 

30° = π/6

45° = π/4

60° = π/3

90° = π/2

120° = 2π/3

135° = 3π/4

150° = 5π/6

180° = π

210° = 7π/6

225° = 5π/5

240° = 4π/3

270° = 3π/2

300° = 5π/3

315° = 7π/4

330° = 11π/6

360° = 2π

Solved Example

Question:

Convert 220° into radian measure.

Solution:

Given,

Degree = 220°

We know that,

Radian =  

\(\begin{array}{l}\frac{degree \times \pi}{180}\end{array} \)

Radian =

\(\begin{array}{l}\frac{220 \times \pi}{180}\end{array} \)

Radian =

\(\begin{array}{l}\frac{11 \times \pi}{9}\end{array} \)

Radian =

\(\begin{array}{l}0.837\end{array} \)

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