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

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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.

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.**