Radian Measure - Definition

[br][size=200][img]data:image/png;base64,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[/img][/size][br][br][i][size=100][size=150][size=200]Where, [br]s = arc length[br]r = radius[br][/size][/size][/size][/i]
Rearrange the arc length formula to find an equation for s/r. [br][br]This is the radian measure, defined as the ratio of the arc length to the radius.
Adjust the angle slider to change the angle measure. What do you notice about the radian measure for each angle?
Adjust the angle measure. What is true about the value of the arc length (s) divided by the radius (r)?
How does this relate to circle similarity?
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Information: Radian Measure - Definition