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Q.

Find the angle measure of 4 radians in degree:


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a

114.591°

b

141.372°

c

229.183°

d

282.743°

e

458.366 

answer is C.

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Detailed Solution

Concept- Use the fact that one complete rotation is equal to 2π radians and also equal to 360°. Use the unitary method to convert 4 radians in degrees.
The angle subtended by the arc of length 1 unit at the center of a circle of radius 1 unit is said to be equal to 1 radian. Hence in this system, one complete angle is equal to 2π radians.
We know that 2π radians are equal to 360°
Then, 1 radian is equal to 360°2π=180°π
So, 4 radians are equal to 180°π×4=229.183°
Therefore, 4 radians are equal to 229.183°
Hence, option 3 is correct.
 
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