Who is asking: Student
If you have an angle you can measure its size in the following way. Draw a unit circle (circle with radius 1) with center at the vertex of the angle.
Measure the length of the arc (counterclockwise) subtended by the angle (the length of the orange arc in the diagram). Suppose that this length is t, then we say that the radian measure of the angle is t radians.
Since the circumference of the unit circle is 2 pi, the 360o angle has radian measure of 2 pi. Likewise 180o is pi radians (half way around the circle). 90o is pi/2 radians and 45o is pi/4. For other angles I remember that
One last point is that if you measure the arc clockwise then the radian measure is negative. Thus -45o is -pi/4 radians.Cheers,