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

neela | High School Teacher | (Level 3) Valedictorian

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To convert 60 degrees to radians:

We know 180 degrees = pi radians.

To convert 156.3 degrees to radians:

To convert 3.1 radians to degrees:

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

giorgiana1976 | College Teacher | (Level 3) Valedictorian

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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:

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:

So 60 degrees represent pi/3 radians.

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

We'll cross multiply and we'll get:

156.34*pi = 180*x

x = 156.34*pi/180

So 156.34 degrees represent 2.7286 radians.

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