HOW TO CONVERT DEGREE TO RADIAN

How to convert degree to radian :

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

Radian measure  =  (π/180) x 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'  =  40   20/60  =  40   1/3 degree

=  121/3 degree

Example 2 :

Solution :

Radian measure  =  (π/180) x degree measure

25° = (π/180) x 25 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

Example 4 :

Solution :

Radian measure  =  (π/180) x degree measure

240° degree  (π/180) x (240) radian

Example 5 :

Solution :

Radian measure  =  (π/180) x degree measure

520 degree  (π/180) x (520) 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

θ1 = 110°  =  (π/180) x (110)  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 degree to radian".

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