Measuring Angles in Radians Activity Alison Nasta Coordinating Seminar

Objectives The students will come up with a definition of a radian. The students will illustrate the relationship between radian measure and degree measure. This activity is suitable for students in an algebra 2 / trigonometry class.

Materials Paper Plates Scissors Ruler String Highlighter

Procedure 1. Divide the class into groups of three students. Each group will be given three different sized paper plates. 2. Fold each of the paper plates into fourths. Outline these crease lines with a highlighter. Label the measures of the angles in between each crease in degrees. 3. Cut a piece of string that is the length of the radius of the paper plate. Cut 6 more pieces of string that are equal in length to the radius.

Procedure 4. Take 1 of these pieces of string and, starting from the center of the paper plate and lying it on one of the creases you outlined, mark where the string touches the end of the plate. Label this point as “0”. 5. Starting at “0”, use another piece of string to measure another length of the radius and mark this new point “1”. Repeat this process until you have labeled 6 points.

Questions 1. Based on your observations, write your own definition of a radian. 2. About how many radians is a straight line? Can you think of a mathematical constant that is close to this number? Compare your results to those of the other students in your group. 3.What effect does the size of the paper plate have on the measurements you obtained in response to the questions asked above? Why do you think this effect occurred? 4.Convert each of the following degree angle measures labeled on your plate into radians. (90, 180, 270, 360) 5.Based on your results and your observations, can you explain the relationship between a radian and a degree? ________ Radians = _________ Degrees 6.What formula could you use to convert degrees to radians? 7.What formula could you use to convert radians to degrees?

Other Questions 1. Convert the following angle measures from degrees into radians. a. 45° b. 231° c. 60° d. 315° e. 135° 2. Convert the following angle measures from radians into degrees. a. π / 12 b. 5π / 4 c. 2.12 d. 11.23 e. 2 π / 3

Connections Calculus: unit circle and trigonometric functions Geometry: measure angles of polygons using degrees Physics: angular measurements (ex. angular speed)

References http://betterlesson.com/document/1445775/degree-and- radian-hands-on-activity-doc http://www.regentsprep.org/Regents/math/algtrig/ATM1/ radianResource.htm