Answer:
see below
Step-by-step explanation:
One radian is equal to the angle formed when the arc opposite the angle is equal to the radius of the circle.
So in sinФ (see attached), the angle Ф is equal to one radian since the arc AB is the same length as the radius of the circle.
Now, the circumference of the circle is 2 PI r, where r is the radius of the circle. So the circumference of a circle is 2 PI larger than its radius. This means that in any circle, there are 2 PI radians.
Therefore 360º = 2 PI radians.
Therefore 180º = PI radians.
So one radian = 180/ PI degrees and one degree = PI /180 radians.
Therefore to convert a certain number of degrees in to radians, multiply the number of degrees by PI /180 (for example, 90º = 90 × PI /180 radians = PI /2). To convert a certain number of radians into degrees, multiply the number of radians by 180/ PI .
