Name: ______________________________________Date_________________________Per._____________

Exploration: Constructing a 1 radian angle

Materials: Concentric Circles, Pipe Cleaner, Protractor

On the handout sheet, there are 6 concentric circles all with center O. The radii of the circles are: 3 cm, 4cm, 5 cm, 6 cm, 8 cm, and 10 cm. You will make four sets of measurements using circles with different radii.

Step 1: Draw a radius from center O to the edge of your circle. Label this point A.

Step 2: Take your pipe cleaner and measure the length of the radius. Bend the pipe to mark the end of radius.

Step 3: Place one end of the pipe at Point A and bend it around the circle counterclockwise, marking the length of the radius as point B on the circle where the pipe ends up.

Step 4: Draw the radius from O to B.

Step 5: Measure ÐAOB using your protractor. Record your measurements.

Step 6: Using the length of your radius (pipe cleaner), measure the circumference of the circle. (How many radius lengths are needed to go around the circle?)

Definition: A central angle has its vertex at the center of the circle and its sides are radii

of the circle. A central angle of a circle has measure 1 radian if it intercepts an arc with the

same length as the radius.

The measure of ÐAOB is 1 radian.

Questions:

1. From your measurements of ÐAOB, a. What is the degree measure of 1 radian? How many degrees are there in one radian?b. Does the degree measure change as you vary the length of the radius?

2. How many radians are there in a complete circle? How many degrees are in a complete circle?

3. How many radians are there in half a circle? How many degrees are in half a circle?

From your text book: Read page 710 the section on the unit circle through Example 4. Work problems 28-50 evens.

B A

O

All Students Birthday between Jan. & June Birthday between July & Dec.Circles of radius 4 and 8 cm 3 cm or 6 cm 5 cm or 10 cm

Find the measure of the angle formed by the hands of a clock at:

a. 3:00 b. 4:30 c. 7:20 d. 1:45