**How to convert degrees to radians in terms of pi :**

To convert from degree to radians, we have to use the formula given below.

(π/180) x (the given degree measure)

Let us look into some examples to know that how to convert the degree measure to radian.

**Example 1 :**

Convert 40° 20' into radian measure

**Solution :**

Radian measure = (π/180) x degree measure

40° 20'

In order to convert 20' to degree, we have to divide it by 60.So, we get

= 40 20/60 = 40 1/3 degree

= 121/3 degree

= (π/180) x (121/3) radian

= (121π/540) radian

**Example 2 :**

Convert 25° into radian measure

**Solution :**

Radian measure = (π/180) x degree measure

25° = (π/180) x 25 radian

Simplifying 25 and 180 using 5 times table, we get

= (π/36) x 5 radian

= (5π/36) radian

**Example 3 :**

Convert -47° 30' into radian measure

**Solution :**

Radian measure = (π/180) x degree measure

47° 30' = 47° 30/60 = 47° 1/2 = 95/2 degree

= (π/180) x (95/2) radian

Simplifying 25 and 180 using 5 times table, we get

= (π/36) x (19/2) radian

= (19π/72) radian

**Example 4 :**

Convert 240° into radian measure

**Solution :**

Radian measure = (π/180) x degree measure

240° degree = (π/180) x (240) radian

Simplifying 25 and 180 using 6 times table, we get

= (4π/3) radian

**Example 5 :**

Convert 520° into radian measure

**Solution :**

Radian measure = (π/180) x degree measure

520 degree = (π/180) x (520) radian

Simplifying 25 and 180 using 2 times table,

= (26π/9) radian

**Example 6 :**

If the arcs of same lengths in two circles subtend angles 65° and 110° at the centre, find the ratio of their radii.

**Solution :**

Let r1 and r2 be the radii of the two circles.

θ1 = 65° = (π/180) x (65) radian

= (π/36) x (13) radian

= (13π/36) radian

θ1 = 110° = (π/180) x (110) radian

= (π/18) x (11) radian

= (11π/18) radian

Length of arc = Radius x Subtended angle

= r1 x (13π/36)

Length of arc = Radius x Subtended angle

= r2 x (11π/18)

r1 x (13π/36) = r2 x (11π/18)

r1/r2 = (11π/18) x (36/13π)

r1/r2 = (11/1) x (2/13)

r1/r2 = 22/13

r1:r2 = 22:13

Hence the ratio of their radii is 22 : 13

After having gone through the stuff given above, we hope that the students would have understood "How to convert degrees to radians in terms of pi".

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