justaguide | Certified Educator

=> 1 degree = pi/180 radians

30 degrees = 30*(pi/180) = 0.5235 radians

131 degrees = 30*(pi/180) = 2.2863 radians

170 degrees = 170*(pi/180) = 2.9670 radians

giorgiana1976 | Student

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:

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:

So 30 degrees represent pi/6 radians.

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

We'll cross multiply and we'll get:

131*pi = 180*x

x = 131*pi/180

So 131 degrees represent 2.285(2) radians.

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

We'll cross multiply and we'll get:

170*pi = 180*x

x = 170*pi/180