Investigating Radian Measure
Become familiar with the interface. Play with the sliders and checkboxes to get an understanding of how things work.
Before continuing, reset the applet by pressing the icon in the upper right corner.
(1) Determine at what angle (in degrees) the arc length from B to C is equal to the radius: ______
(2) Definition: radians is a unit of angular measure, similar to degrees. One radian is equal to an angle at the center of a circle whose arc is equal in length to the radius. Thus, from (1), we can conclude: 1 radian ≈ ______ degrees (set θ equal to the angle above and click the checkbox for “Show radian measure?” to verify).
(3) Change the radius to different values. How does it affect the radian measure? What is the relationship between the arc length and the radian measure?
(4) What is the degree measure of the angle that creates a semicircle? _______ What is the radian measure of the same angle? ________
(5) What is the degree measure of the angle that creates a full circle? _______ What is the radian measure of the same angle? ________
(6) Set the radius to 1 and click the checkbox for “Show Circumference?” Look at a few different angles and make a hypothesis on the relationship between radian measure and circumference.
(7) Recall the radian measure for a full circle: ________ What is the circumference when the radius is 1? ________
(8) From (7), make a conclusion about how many radians are in a full circle.