Convert the following : 60 degrees to radians, 156.34 degrees to radians, 3.1 radians to degrees.

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neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

To convert 60 degrees to radians:

We know 180 degrees = pi radians.

60 degrees = (60/180)pi radians = pi/3 radians = 1.0472 radians.

To convert 156.3 degrees to radians:

180 degrees = pi radians, therefore 156.3 deg = (156.3)pi/180 radians.

156.3 degrees =  2.7279 radians.

To convert 3.1 radians to degrees:

Pi radians = 180 degrees.

Therefore 3.1 radians = (3.1*180/pi ) degrees.

3.1 rad = 177.6169 degrees.

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 60 degrees to radians:

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

x radians................................60

We'll cross multiply and we'll get:

60*pi = 180*x

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

x = 60*pi/180

We'll simplify and we'll get:

x = pi/3 radians

So 60 degrees represent pi/3 radians.

Now, we'll convrt 156.34 degrees to radians using proportions also.

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

x radians................................156.34

We'll cross multiply and we'll get:

156.34*pi = 180*x

x = 156.34*pi/180

x = 2.7286 radians

So 156.34 degrees represent 2.7286 radians.

The inverse conversion is going from radians to degrees, so we'll apply proportions, too.

3.1 radians to degrees

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

3.1 radians................................x

Notice that the unknown x is located below 180 degrees.

x*pi = 3.1*180

x = 3.1*180/pi

x = 177.62 degrees

So 3.1 radians represent 177.62 degrees.

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