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