MEASURE OF AN ANGLE

READ the instructions on the right and INTERACT with the GeoGebra applet below.

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Steven Lapinski, October 2007 Created with GeoGebra

Investigation Steps

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  • 1. What are the measures of the blue radius and the red arc?

  • 2. Move point A and observe: What measurements change? What measurements stay the same?

  • 3. Move point P until the measure of the arc equals the radius. This measure correspondes to 1 radian.

  • 4. What angle is bigger, the one that measures 1 radian or one that measures 60°?

  • 5. Move Point P so that the angle measures 2 radians, how many degrees would that be? Would an angle of 3 radians be greater or less than 180°?

  • 6. In your own words, write a definition of a radian.

  • 7. Imagine a 180° angle, what is the measure in radians? Is this reasonable? How many radians is a 90° angle? A 360°? why?