# Convert the following: 40 degrees to radians, 100 degrees to radians, 2.5 radians to degrees, 3 radians to degrees.

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### 2 Answers

To convert between radians and degrees just keep in mind that 2*pi radians is equal to 360 degrees.

Therefore we get 1 radian = (360/2*pi) degrees and 1 degree = 2*pi/360 radian

To convert any angle given in radians to degrees multiply it by 360/2*pi and to convert any angle given in degrees to radians multiply it by 2*pi/360.

Now, to convert the values that you have given:

40 degrees = 40*(2*pi/360) radian = 2*pi/9 = 0.6981 radians

100 degrees = 100*(2*pi/360) radian = 5*pi/9 = 1.745 radians

2.5 radians = 2.5*(360/2*pi) degrees = 143.2394 degrees

3 radians = 3*(360/2*pi) degrees = 171.8873 degrees.

We know that 2pi radians = 360 degree.

pi = 3.141592654 .

Therefore 1 rad = 360/2pi = 57.29577951 degree.

Also 1 degree = 2pi/360 = 0.017475292.

So while converting degrees to radians we multiply by the number 0.017475292.

Therefore ,

40 degree = 40*0.017475292 = 0.6981 radians nearly.

100 degrees = 100*0.017475292 radians = 1.01745 radians.

While converting radians to degrees, we multiply by 57.29577951.

So,

2.5 radians = 2.5*57.29577951 degrees = 143.2394 degrees.

3 radians = 3*57.29577951 degree. = 171.8873 degrees.