Radians.Convert from degrees to radians : 30;131;170.

2 Answers | Add Yours

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

180 degrees = pi radians

=> 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'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 30 degrees to radians:

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

x radians................................30

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:

x = pi/6 radians

So 30 degrees represent pi/6 radians.

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

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

x radians................................131

We'll cross multiply and we'll get:

131*pi = 180*x

x = 131*pi/180

x = 2.2852(2) radians

So 131 degrees represent 2.285(2) radians.

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

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

x radians................................170

We'll cross multiply and we'll get:

170*pi = 180*x

x = 170*pi/180

x = 2.96(5) radians

So 170 degrees represent 2.96(5) radians.

We’ve answered 318,936 questions. We can answer yours, too.

Ask a question