Move the slider to change the radius length.[br]Move point P until the measure of the radius is the same as the length of the arc.

1. What are the measures of the radius and the purple arc?[br]2. How many times larger is the arc of a 360 degree angle than the radius?[br]3. Move point P until the measure of the arc equals the radius. This measure correspondes to 1 radian.[br]4. Move the slider "a" and observe: What measurements change? What measurements stay the same?[br]5. What angle is bigger, one that measures 1 radian or one that measures 60 degrees?[br]6. Imagine an angle that measures 2 radians, how many degrees would that be? How about 5 radians? 1/2 radian? Check your answers in the construction.[br]7. In your own words, what is a radian?[br]8. Imagine a 180 degrees angle, what is the measure in radians? Is this reasonable? How many radians is a 90 degree angle? A 360 degree? why?