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I want to make function a[t] a continuous which has indeterminate form at some points.

tT = 0.0042643923240938165;  

y[t_] := (1625.0688606154426*Cos[1473.4069545336129*t]*Cos[0.9403762801519631*Tanh[2.4*Sin[1.2636183784438946 + 1473.4069545336129*t]]])/
    Sqrt[1 - 0.48999999999999994*Sin[1473.4069545336129*t]^2];  

z[t_] := -((1625.0688606154426*Cos[1473.4069545336129*t]*Sin[0.9403762801519631*Tanh[2.4*Sin[1.2636183784438946 + 1473.4069545336129*t]]])/
     Sqrt[1 - 0.48999999999999994*Sin[1473.4069545336129*t]^2]);  

NSolve[{y[t] == 0, z[t] == 0}, t]  

a[t_] = If[y[t] == 0 && z[t] == 0, 0, Sin[2*ArcTan[y[t], z[t]]]];  

Plot[a[t], {t, 0, tT}, ImageSize -> Large] 

At some point t=0.0010661 both y[t] and z[t] becomes zero. So i gave If condition when ever y[t] and z[t] both are zero take the value to be zero. It is not working.
Any suggestion how to make this function continuous. Thank you.

enter image description here enter image description here

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  • $\begingroup$ I cannot reproduce your discontinuity in version 10.0 for linux. Which version are you using? $\endgroup$ – mattiav27 Nov 29 '19 at 9:27
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    $\begingroup$ @mattiav27 Probably because of the improvement of singularity detection in v11. Adding Exclusions->None helps. Related: mathematica.stackexchange.com/a/143728/1871 $\endgroup$ – xzczd Nov 29 '19 at 9:48
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Try this one

p = 0.9403762801519631;
q = 2.4;
r = 1.2636183784438946;
s = 1473.4069545336129;
Clear[f]
f[t_] := -Sin[2 p Tanh[q Sin[r + s t]]]

instead of a[t].

| improve this answer | |
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  • $\begingroup$ Thanks a lot. now i'm trying to use this /. ArcTan[Tan[x_]] -> x at the end of my equation. Not sure whether it will cause any error. Though to tell you. $\endgroup$ – Gummala Navneeth Nov 29 '19 at 12:06

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