M2 radian plz help 20點!!!

2014-02-14 5:31 am
s = rθ, where θ is measured in radians.

unit of s is cm but unit of θ is radian. Why is it still correct.

回答 (1)

2014-02-14 4:08 pm
✔ 最佳答案
Arc length, s = 2πr x θ/360 degree, where θ is in degree and r in cm. Therefore unit of s is in cm.
Since 360 degree = 2π radian, so s = 2πr x θ/2π = rθ where θ is now in radian and r is stil in cm. Therefore s is still in cm.
(Note : same case happens to area of sector,
A = πr^2 x θ/360 in degree = πr^2 x θ/2π in radian = r^2θ/2 in radian.)

2014-02-14 08:23:22 補充:
For example :
θ = 90 degree and r = 5 cm. So s = 2πr x 90/360 = 2π(5) x 1/4 = 5π/2 cm.
90 degree = π/2 radian, so s = r θ = 5 x (π/2) = 5π/2 cm.


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