p=71;q=52;a=p/q;PolarPlot[-a*Sin[t]+Sin[a*t],{t,0,2*q*Pi}]

Integrate[Sin[t]^2/(1+Sin[t])^3,{t,0,tt}]

Integrate[Sin[t]^2/(1-Sin[t])^3,{t,0,tt}]

FullSimplify[Integrate[1/(1+Sin[t]/Pi),{t,0,Pi},Assumptions->k<1&&k>0]/.Pi->1/k]

Integrate[1/(1+Sin[t]k),{t,0,Pi},Assumptions->k>1]

A=Integrate[Sin[t]^2/(1+Sin[t]k)^3,{t,0,Pi},Assumptions->k>1]

A=Integrate[Sin[t]^2/(1+Sin[t]k)^3,{t,0,Pi},Assumptions->k<1&&k>0]

Integrate[2 c Sin[t]^2/(1+Sin[t]Sin[u])^3,{t,0,Pi}]

FullSimplify[c ((Sec[u])^5) (-2 (ArcTan[Cot[(u/2)]]-ArcTan[Tan[(u/2)]]) (-2+Cos[2 u])-3 Sin[2 u])]

Limit[-2/(ArcCos[k]+2*ArcCos[k]*k^2-3*k*(1-k^2)^(1/2))^(1/2)/g^(1/2)*(1-k^2)^(3/4)*ArcCos[k],k->1]

-2/(ArcCos[k]+2*ArcCos[k]*k^2-3*k*(1-k^2)^(1/2))^(1/2)/g^(1/2)*(1-k^2)^(3/4)*ArcCos[k]