in A level FM, why is it that a straight line has pi radians?Watch
a radian is a measure of an angle, just like degrees. to get from degrees to radian you multiply by π and divide by 180. and from radian to degrees is multiply by 180 and divide by π.
so 1π = 180*
since a straight line is straight, it has an angle of 180, so π rad
its slightly less than 60 degrees.
In a sense, defining an angle in terms of a known length makes more sense than a fairly arbitrary split into 360 degrees.
If you have a sector of a circle (like a piece of cake) where the arc length (ie the curved edge) is the same length as the straight side(s), equal to radius of course, then the angle subtended from the centre of the circle is defined as 1 radian.
Other replies explain how to convert between degrees and radians which is what you will need to know.
However there are good reasons to work with radians.
In geometry the circumference of a circle is 2 pi r and the length of an arc is r x angle, but only if the angle is measured in radians.
In calculus, the derivative of sinx is cosx, but only if you're working with radians. The correct formula when using degrees would be much more messy. Similarly the usual Taylor series that define sinx and cosx work when you're using radians.