What is a radian?
Use the following applet to answer the questions below to discover what a radian is. Hint: Enable the ratio box and see what conjectures you can form.
Use the following applet to answer the questions below to discover what a radian is. Hint: Enable the ratio box and see what conjectures you can form.
Notice that the central angle is not being measured in degrees, it is labeled in terms of radians. Radians are another unit of measure for angles. You will explore the application to find how we can convert from one type of unit to the other and determine a definition of a radian.
1) Move point \(B\) so that the arc length is \(0\). What is the radian measure of the central angle intercepting the arc with length \(0\)?
2) Move point \(B\) so that the arc length is the same as the radius of the circle. What is the radian measure of the central angle intercepting the arc with the same length as the radius? You can drag the center of the circle to change the radius to see if this relationship still holds.
3) Move point \(B\) so the arc length is half of the circle. What is the radian measure of the central angle now?
4) A full circle has measure \(360˚\), how many radians does this correspond to?
5) Fill in the following blanks
\(\pi\) radians =_______ \(^\circ\)
\(\pi /2\) radians =_______ \(^\circ\)
________radians = \(45 ^\circ\)
________radians = \(30 ^\circ\)
6) In your own words, define what a radian is.
7) How can you convert an angle measure given in radians to an angle measure in degrees?
8) How can you convert an angle measure given in degrees to an angle measure in radians?