Determine the length of the arc (in radian measure) and the measure of the angle (in radian and degree measures) generated by a point that starts from (1,0) and terminates at the following: 1. Positive x-axis 2. Negative x-axis 3. Positive y-axis 4. Negative y-axis Hint: Recall that the unit circle circumference is 2π units. Thus, if the unit circle is to be divided into "n" congruent arcs, then the measure of each arc is equal to 2π/n units. (If the point which moves from (1,0) terminates at (0,1), then the length of the arc generated by the point is π/2 units and the measure of the central angle t is also equal to π/2 or equivalent to 90°. Similarly, if the point terminates at π/4, then the length of the arc is π/4 units and the measure of the central angle is π/4 or 45°.)
Determine the length of the arc (in radian measure) and the
measure of the angle (in radian and degree measures) generated by a point
that starts from (1,0) and terminates at the following:
1. Positive x-axis
2. Negative x-axis
3. Positive y-axis
4. Negative y-axis
Hint: Recall that the unit circle circumference is 2π units. Thus, if the unit circle is to be divided into "n" congruent arcs, then the measure of each arc is equal to 2π/n units.
(If the point which moves from (1,0) terminates at (0,1), then the length
of the arc generated by the point is π/2
units and the measure of the central
angle t is also equal to π/2 or equivalent to 90°. Similarly, if the point terminates at π/4, then the length of the arc is π/4 units and the measure of the central angle
is π/4 or 45°.)
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