Morgan Park High School · Web view2011/04/07 · A central angle of a circle has measure 1 radian...
Transcript of Morgan Park High School · Web view2011/04/07 · A central angle of a circle has measure 1 radian...
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