Is Calculating Radian Measure from Arc Length and Radius Correct?

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SUMMARY

The calculation of the radian measure of a central angle theta, subtended by an arc length of 20 cm on a circle with a radius of 2 m, is confirmed to be correct. The formula used, S = r(theta), where S is the arc length and r is the radius, leads to the equation 20 = 200(theta). Solving this gives theta = 0.1 radians. The result is valid, as the arc length is indeed small compared to the radius.

PREREQUISITES
  • Understanding of the formula S = r(theta) for arc length and central angles
  • Knowledge of converting between centimeters and meters
  • Basic trigonometry concepts related to radians
  • Familiarity with circle geometry
NEXT STEPS
  • Study the relationship between arc length and central angles in circles
  • Learn about converting units between centimeters and meters
  • Explore additional examples of calculating radian measures
  • Investigate the applications of radians in trigonometry and calculus
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Students studying geometry, mathematics educators, and anyone interested in understanding radian measures and their applications in circular motion.

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A central angle theta is subtended by an arc 20cm long on a circle of radius 2m, find the radian measure of theta.

i used the formula S=r(theta), and just plugged in what was given.

20=200(theta), from there i got theta= 20/200, which gives me an answer of .1. I thought i did this correctly but my answer seems kind of weird. Did i do this correctly?
 
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jayjohn28 said:
A central angle theta is subtended by an arc 20cm long on a circle of radius 2m, find the radian measure of theta.

i used the formula S=r(theta), and just plugged in what was given.

20=200(theta), from there i got theta= 20/200, which gives me an answer of .1. I thought i did this correctly but my answer seems kind of weird. Did i do this correctly?

that should be correct. 200cm in relation to 2ocm arc is small
 

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