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1. Cut out a large circle or use a large paper plate.
2. Fold the circle in half to get one diameter. (Fold
3. Fold the circle in half again to get another
diameter (Fold 2).
4. Draw in the x- and y-axis. Label the radius as 1
unit. Label the coordinates of the points and their radians. Complete the
5. Refold the circle to position of Fold 2. Fold the
quarter circle again in half. Draw in this lines. Each of these new lines
is at from the original x- or
y-axis. In the first quadrant, drop a vertical line segment from the
endpoint of the radius. What special triangle has been formed? Use this to
calculate the sides of the right triangle. This should help you name the
coordinates for this endpoint. Thinking about reflections over the x- and
y-axis, name the coordinates of the endpoints for the other radii.
6. Label the coordinates of the points. Label their
radians also. Complete the chart below.
7. Refold the circle to the position of Fold 2. Once
you have the quarter of a circle, fold the quarter into thirds. This can
be done by folding one piece inside the other until you have 3 equal
pieces overlapping. Open the circle or plate. Notice how each quadrant has
been divided. Notice there are not 4 equal pieces in each quadrant. Create
right triangles in the first quadrant from the endpoint of each radius.
What special right triangle has been formed? Calculate the length of each
side of the special triangle.
8. Draw in these 4 lines. Label these new points.
Identify the radian measure also. Complete the chart below for these eight
9. Recall that the coordinate of each endpoint on the
unit circle is (cos A, sin A). Use this unit circle to help you recall the
values in the table for Trigonometric
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© Rahn, 2000