Radians and Arc Length (Grades 11-12)

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Radians and Arc Length

On the unit circle (radius of 1) the arc length from [math]0deg[/math] to [math]90deg[/math] is
Unit Circle Complete
  1. [math]90[/math]
  2. [math]pi/2[/math]
  3. [math].25[/math]
  4. [math]pi[/math]
[math]720deg[/math] is equivalent to how many radians?
  1. [math]4pi[/math]
  2. [math]pi/4[/math]
  3. [math]2pi[/math]
  4. [math]pi/2[/math]
Draw an angle which is [math](5pi)/3[/math] radians and the arc which subtends it.
Unit Circle Blank

The arc length around a unit circle has the same value as the arc angle, in radians, that it subtends.
  1. True
  2. False
An arc length of 2.62 m on a circle with a radius of 1 m would subtend and arc angle of how many radians?
  1. [math]pi/2[/math]
  2. [math](5pi)/3[/math]
  3. [math](5pi)/6[/math]
  4. [math](7pi)/6[/math]
How many radians are equivalent to [math]315deg[/math]?
  1. [math]pi[/math]
  2. [math](7pi)/4[/math]
  3. [math](7pi)/6[/math]
  4. [math](5pi)/4[/math]
Fill in the missing measurements for both degrees and radians at each blank around the unit circle. You may leave the ordered pairs blank.
Unit Circle Fill-In

[math]45deg[/math] and [math]pi/6[/math] radians are equivalent angles.
  1. True
  2. False
A circular pathway is created with a diameter of 20 feet. If the pathway makes an arc of [math]210deg[/math] how long is the pathway?
  1. [math]210 \ "ft"[/math]
  2. [math](7pi)/6[/math]
  3. [math](35pi)/3 \ "ft"[/math]
  4. [math]35 \ "ft"[/math]
A swing at the playground is suspended by chains that are 10 feet long. Every time that a child swings from the highest point on one side to the highest point on the other side the swing travels a distance of 10.5 feet. What arc angle, in radians, is the child raveling each time the swing travels in one direction?
  1. [math]pi/2[/math]
  2. [math](3pi)/2[/math]
  3. [math](2pi)/3[/math]
  4. [math]pi/3[/math]

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