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Radians to Degrees:

Radians and degrees are two different measuring systems, which are used to measure the angle. The SI unit of angle is the radian. One radian would be written as 1 rad, or simply 1. And, one degree would be written as 1°. We can convert between radian and degree using the following formula.


t=πx/180°                                                                      x=180°t/π

 

Radians to Degrees Sample Questions:

Question 1: Write π/3 radians in degrees.


Answer: 60°

Explanation: Plug the value in the formula.

 

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Question 2: Write 3π/2 radians in degrees.


Answer: 270°

Explanation: Plug the value in the formula.

 

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Question 3: Convert 30° into radians. Write in terms of π.
 

Answer: π/6

Explanation: Plug the value of the angle in radianss.

 

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Question 4: Convert 120° into radians. Write in terms of π.


Answer: 2π/3

Explanation: Plug the value of the angle in radians.

 

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Question 5: In a circle, having a center at O, COD=5π/4. Write this measure in terms of degrees.


Answer: 225°

Explanation: Plug the value in the formula

 

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Question 6: In a circle, having a center at O, BOD=150°. Write this measure in terms of radians.


Answer: 5π/3

Explanation: Plug the value of the angle in radians.

 

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Question 7: Convert 5 radians to degrees.


Answer: 286.62°

Explanation: Plug the value in the formula.

 

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Question 8: Convert 75° into radians.


Answer: 1.3

Explanation: Plug the value of the angle in radians.

 

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Question 9: Convert 440° into radians.


Answer: 7.68

Explanation: Plug the value of the angle in radians.

 

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Question 10: Convert 9 radians to degrees. Use π =3.14


Answer: 515.92°

Explanation: Plug the value in the formula

 

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Frequently Asked Questions:

Question 1: How to convert radians to degrees?

Angle is measured in degree and radians. One complete angle is equal to 2π in radian form and 360° in degrees form. So, relation between radian and degree is

 


2π radians = 360° and


π radians = 180°


1 Radian = 180°/π

 

Question 2: When to use degrees or radians?

Angle is a part of a circle and a circle's diameter is equivalent to the radian. We want to make sure we are talking about (C=πD or C=2πr=C/r =2π) ratio whether we're working with circles or portions of circles. As a result, the word radians is always used to represent this ratio.

 

Question 3: How many radians is 180°?

One complete angle is equal to 2π in radian form and 360° in degrees form. So, relation between radian and degree is


360°=2π radians 

180°=π radians

 

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