Plot[ ((0.9286 * Sign[ Sin[Pi/2 t] ]*(z -1/5 z^2 -3/175 z^3 -23/7875 z^4 -(62.47 z^5 +15.04 z^6 +3.895 z^7 +1.061 z^8)/100000)) /. (z -> (Abs[ 1.509 * ArcSin[ Sin[Pi/2 t] ] ])^(2/3) )), { t,0,10 } ]