find arc length of a circle with a radius of 5 and a central angle of 7 rad.

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find arc length of a circle with a radius of 5 and a central angle of 7 rad.

Mathematics
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|dw:1444528017439:dw|
|dw:1444528026996:dw| \[\Large \text{Arc length} = \frac{\text{radian angle}}{2\pi \ \text{radians}}*(\text{circumference})\] \[\Large S = \frac{\theta}{2\pi}*(2\pi*r)\] \[\Large S = \frac{\theta}{\cancel{2\pi}}*(\cancel{2\pi}*r)\] \[\Large S = \theta*r\]
The formula \(\Large S = \theta*r\) works only if \(\Large \theta\) (greek letter theta) is in radians

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correct
thanks
hmm something is off though, I think theta needs to be restricted
the formula only works if theta is between 0 and 2pi
7 radians = 7*(180/pi) = 401.070456591577 degrees approximately this angle is over 360 degrees so what needs to happen is you need to find the reference angle to 7 radians |dw:1444528584599:dw|
|dw:1444528610304:dw|
does it really say "7 radians" ? or is it some fraction with pi in it?
it says 7 rads
hmm so strange. Usually the central angle is something between 0 and 2pi
off topic, but |dw:1444529191578:dw| what does the "w" STAND FOR?
v = linear velocity w (some books use \(\Large \omega\) which is the greek letter omega) = angular velocity r = radius
thanks
the angular velocity or speed is how fast the object is revolving around a fixed center point one example of an angular velocity is pi radians per second. Each second, the object rotates pi radians or 180 degrees
no problem

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