Radians & Degrees .

Date January 2006
Class Trigonometry
Teacher Janet Wineland

This semester I have a Trigonometry Class.  In the past, I have had a difficult time getting them to understand radian measurement.  This year I started the first day (we have 90 min. class periods) talking about the unit circle using degree measurement.  We discussed the 90, 180, 270 and 360-degree positions and the rotation of angles.  I then handed each student a piece of string, scissors and a paper with a circle drawn on it.  The circles were all different sizes and I have 32 students in this class so we had quite a variety.  I had them cut the string the length of the radius and use it to mark the circle all the way around.  I had a big circle at the front of the room for demonstration.  We talked about the circumference formula and managed to get pi and 2 pi marked on the circle.  All of a sudden they could see that pi was 3.12 of the radius’ they had marked on their circle.  The rest of the discussion followed smoothly.  We often switch back and forth between radian measure and degree measure and it is going great!  For the first few days I would hear comments between students like:  “3 rads – remember the yellow circle – that is close to pi “  or “5 rads is in the fourth quadrant”.
I thought this was a great way to introduce the idea of radian measurement.  I was real hesitant to do this with such a large class – but it couldn’t have gone any better!  That activity is in my lesson plans permanently. 

Date Sept. 2005
Class applied trigonometry
Teacher Ray Weier

We had been working the previous class period with measuring angles in degrees and how to convert from decimal degrees to degree minute second form. 

During this lesson, I introduced the concept of radian measure.  I used the top of an ice cream bucket for my circle and then using pieces of yarn equal in length to the radius of my circle I demonstrated and then had them try to see how many of these radii they were able to wrap around the circle.  Most came up the answer that there were a “little more than 6” of them.  I then demonstrated to them algebraically that there were actually 2p radians needed to go entirely around the circle.

We then looked at formulas for converting from degrees to radians and also from radians to degrees.  As a way to help them remember the conversion formulas, I then gave them a worksheet.

We went through coding in the first program together with each student using his/her own calculator.  Most of the students had never typed in a program on a calculator before, but we took our time and everyone seemed to pick the keystrokes up pretty quickly.  I think that having them actually see the program code helped them to see why you need to use variables in mathematics sometimes.

Using the first program as a guide, they all were able to write the code for the second program quite easily.  They also did not have too much difficulty entering the second program on the calculators and all were able to get their programs debugged and running.

We did have a discussion about what we should use for test data for each program and the importance of using test data.

Overall, I think that the activity went well.  I really feel that it is good to have the students write calculator programs from time to time since it causes them to use logical thinking skills and gives them experience working with the concept of variables.