Convert from degrees to radians : 30;131;170.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We have to convert 30 , 131 and 170 from degree to radian.

Now we know that 2*pi radians is equal to 360 degrees.

Therefore we get 1 degree = 2*pi/360 radian

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

Now to convert 30 degrees to radian : 30*(2*pi/360) = .5235 radians

To convert 131 degrees to radian : 131*(2*pi/360) = 2.2863 radians

To convert 170 degrees to radian : 170*(2*pi/360) = 2.9670 radians

Therefore 30 degrees is equal to 0.5235 radian, 131 degrees is equal to 2.2863 radians and 170 degrees is equal to 2.9670 radians.

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neela | High School Teacher | (Level 3) Valedictorian

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To convert the degrees 30, 131 and 170 into radians.

We know that 2pi radians. = 360 degres.

Therefore 1 degree = 2pi/360 radians .

Or 1 degree = pi/180 radians.

pi = 3.141582654.

Therefore 1 degree = pi/180 = 0.01753292.

Therefore to convert any degree into we multiply by 0.01753292.

Thus 30 degree = 30* 0.01753292 =  0.5236radians nearly.

131 degree = 131*0.01753292 = 2.2864 radians nearly.

170 degree = 170*0.01753292 = 2.9671 radians nearly.

Top Answer

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

Let's recall that the circumference of a circle is given by the formula:

C = 2pi*r, where 2pi represents one revolution of a circle.

2pi = 360 degrees

We'll divide by 2:

pi = 180 degrees

Starting from this result and using proportions, we'll convert radians in degrees and degrees in radians.

 We'll convert 30 degrees to radians:

pi radians............................ 180

x radians................................30

We'll cross multiply and we'll get:

30*pi = 180*x

We'll divide by 180 and we'll use symmetric property:

x = 30*pi/180

We'll simplify and we'll get:

x = pi/6 radians

So 30 degrees represent pi/6 radians.

Now, we'll convrt 131 degrees to radians using proportions also.

pi radians............................ 180

x radians................................131

We'll cross multiply and we'll get:

131*pi = 180*x

x = 131*pi/180

x = 2.2852(2) radians

So 131 degrees represent 2.285(2) radians.

Now, we'll convrt 170 degrees to radians using proportions also.

pi radians............................ 180

x radians................................170

We'll cross multiply and we'll get:

170*pi = 180*x

x = 170*pi/180

x = 2.96(5) radians

So 170 degrees represent 2.96(5) radians.

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