## anonymous one year ago find arc length of a circle with a radius of 5 and a central angle of 7 rad.

1. jim_thompson5910

|dw:1444528017439:dw|

2. jim_thompson5910

|dw:1444528026996:dw| $\Large \text{Arc length} = \frac{\text{radian angle}}{2\pi \ \text{radians}}*(\text{circumference})$ $\Large S = \frac{\theta}{2\pi}*(2\pi*r)$ $\Large S = \frac{\theta}{\cancel{2\pi}}*(\cancel{2\pi}*r)$ $\Large S = \theta*r$

3. jim_thompson5910

The formula $$\Large S = \theta*r$$ works only if $$\Large \theta$$ (greek letter theta) is in radians

4. anonymous

so 35? @jim_thompson5910

5. jim_thompson5910

correct

6. anonymous

thanks

7. jim_thompson5910

hmm something is off though, I think theta needs to be restricted

8. jim_thompson5910

the formula only works if theta is between 0 and 2pi

9. jim_thompson5910

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|

10. jim_thompson5910

|dw:1444528610304:dw|

11. jim_thompson5910

does it really say "7 radians" ? or is it some fraction with pi in it?

12. anonymous

13. jim_thompson5910

hmm so strange. Usually the central angle is something between 0 and 2pi

14. anonymous

off topic, but |dw:1444529191578:dw| what does the "w" STAND FOR?

15. jim_thompson5910

v = linear velocity w (some books use $$\Large \omega$$ which is the greek letter omega) = angular velocity r = radius

16. anonymous

thanks

17. jim_thompson5910

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

18. jim_thompson5910

no problem