Why the angle has to be smaller than 5 degree to be able to satisfy the small angle approximation?

Why 5.5 can not be a small angle? Does 5 a magic number???

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students can key in 5/180*PI = 0.08726

in radian mode, students can key in sin(5/180*PI) = 0.08715

the students can realise the approximation is accurate for 2 decimal place only.

students can key in 5.5/180*PI = 0.09599

in radian mode, students can key in sin(5.5/180*PI) = 0.09584

the students can realize the approximation is accurate for 2 decimal place only.

it is a balance between practically observably angle of oscillation and accuracy in approximation of the assumption of

[quote author=Fu-Kwun Hwang link=topic=2010.msg7633#msg7633 date=1292557129]

i don't understand the question on "damping factor are the same for all pendulums"

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What I mean is "The period and damping rate are the same for all pendulums."

ic damping rate.

then my earlier answer is acceptable? made to obey this mathematical equation?