Show that the period ( time for one complete swing back wards and for wards of a pendulum T=√L(costeta)/g is only true for small angle almost less than one radian.
If you go thru the proof on an energy basis, you have to set initial KE to final KE eventually, and in that analysis, you will deal with tangent or sine of the angle of swing, and you will have to ASSUME the angle and it's sine and it's tangent are all equal. That is only true for small angles. Remember the restoring force (gravity) is mg*sinTheta, and eventually, one will have to convert SinTheta to some set of angles over the arc swing distance.
