Understanding Radians (Grades 11-12)

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Understanding Radians

1. 
Radians can only be used to measure central angles of the unit circle.
  1. True
  2. False
2. 
The measure, in radians, of a central angle of a circle is determined by the length of the arc subtending the angle and the length of the radius of the circle. Therefore, the units used to measure these two lengths will affect the angle's unit of measure.
  1. True
  2. False
3. 
For any circle, the measure of a central angle which is subtended by an arc of equal length to the radius of that circle will ALWAYS be 1 radian.
  1. True
  2. False
4. 
If an angle is not part of a circle, radians cannot be used to measure it.
  1. True
  2. False
5. 
If an angle is measured in radians, the symbol [math]pi[/math] must appear in the measurement.
  1. True
  2. False
6. 
The length of [math]\stackrel{\frown}{ACB}[/math] divided by the length of [math]bar{OB}[/math] gives the measure of what angle in radians? Assume that [math]O[/math] is the center of the circle and points [math]A, O[/math], and [math]B[/math] are collinear.
Circle ABC
  1. [math]ang COB[/math]
  2. [math]ang CAB[/math]
  3. [math]ang BOA[/math]
  4. None of the above.
7. 
For the circle pictured, with center O (not labeled), what is the measure of [math]ang AOB ?[/math] Choose all correct answers. Assume that points [math]A, O, B[/math] are collinear.
Circle with Diameter AB
  1. [math]180°[/math]
  2. [math]0°[/math]
  3. [math]pi[/math]
  4. [math]pi/2[/math]
8. 
If [math]CO = 5 \ "cm"[/math] and [math] l \stackrel{\frown}{BC} = 10 \ "cm"[/math], what is [math]m ang COB ?[/math] The diagram is not drawn to scale.
Circle ABC
  1. It cannot be determined with this information.
  2. 60°
  3. 2 rad
  4. 0.5 rad
9. 
Which of the following equations, found by rearranging the equation for the circumference of a circle, [math]C = 2 pi r[/math], gives the number of radians of a half rotation?
  1. [math]1/2 C = pi r[/math]
  2. [math](2C)/r = pi[/math]
  3. [math]C r = 2 pi[/math]
  4. [math](1/2 C)/r = pi[/math]
10. 
There are two circles, circle A and circle B. The radius of circle B is twice the length of the radius of circle A. Let [math]s_A[/math] be the length of an arc on circle A and [math]s_B[/math] be the length of an arc on circle B. If [math]s_B = 2s_A[/math], what can be said about the two angles subtended by these arcs, [math]theta_A[/math] in circle A and [math]theta_B[/math] in circle B?
  1. [math]theta_A = 2 theta_B[/math]
  2. [math]theta_A = 1/2 theta_B[/math]
  3. [math]theta_A = theta_B[/math]
  4. No conclusion can be made without knowing the actual lengths of the radii and arcs.

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