HOW TO CONVERT DEGREES TO RADIANS

Example 1 :

Convert 40° 20' into radian measure.

Solution :

Radian measure = (π/180°) x degree measure

40° 20' = 40²⁰⁄₆₀ degrees

= 40⅓ degrees

= 121/3 degrees

= (π/180°) x (121/3) radians

= (121π/540) radians

Example 2 :

Convert 25° into radian measure.

Solution :

Radian measure = (π/180°) x degree measure

25° = (π/180°) x 25 radian

= (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' = 47³⁰⁄₆₀ degrees

= 47½ degrees

= 95/2 degrees

= (π/180°) x (95/2)° radians

= 19π/72 radians

Example 4 :

Convert 240° into radian measure.

Solution :

Radian measure = (π/180°) x degree measure

240° = (π/180°) x 240° radians

   = 4π/3 radian

Example 5 :

Convert 520° into radian measure 

Solution :

Radian measure = (π/180°) x degree measure

520° = (π/180°) x 520° radians

= 26π/9 radians 

Example 6 :

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

Solution :

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

θ₁ = 65° = (π/180°) x 65° radians 

= 65°π/180°  radians

= 13π/36 radians

θ₁ = 110° = (π/180°) x 110° radians

= 110°π/180° radians

= 11π/18 radians

Length of arc = Radius x Subtended angle :

 = r₁ x (13π/36)

And also,

= r₂ x (11π/18)

Given : Arcs are in same length.

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.

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