Definition of Radian and Angle Conversion

This GeoGebra applet visually demonstrates the definition of the radian measure and its conversion to degrees. By dynamically showing the ratio of arc length to radius, it helps users deeply understand the geometric meaning of radians. The interface includes interactive circles, arcs, rotation angles, and a conversion table for degrees and radians covering common angles such as right angles, straight angles, full rotations, and special angles. This makes it ideal for beginners in trigonometry and analytic geometry to explore and learn interactively. Users can manipulate the angle of rotation on an interactive circle and observe in real time how the corresponding arc length changes relative to the radius. This dynamic visualization reinforces the core definition of a radian: the central angle subtended by an arc whose length equals the radius of the circle. As students drag the angle slider, they see that one radian corresponds to an arc length equal to the radius, and that a full rotation equals 2 pi radians or 360 degrees. The accompanying conversion table provides quick reference values for frequently encountered angles, helping learners build intuition and fluency in switching between degree and radian measures. This applet is especially valuable for students encountering radians for the first time, as it connects the abstract formula to concrete geometric reasoning and supports discovery-based learning in trigonometry and analytic geometry courses.