f⁽⁰⁾(x)=sin(x)-x+x³/3!; f⁽⁰⁾(0)=0
f⁽¹⁾(x)=cos(x)-1+x²/2!; f⁽¹⁾(0)=0
f⁽²⁾(x)=-sin(x)+x; f⁽²⁾(0)=0
f⁽³⁾(x)=-cos(x)+1; f⁽³⁾(0)=0
f⁽⁴⁾(x)=sin(x); f⁽⁴⁾(0)=0
f⁽⁵⁾(x)=cos(x); f⁽⁵⁾(0)=1
f⁽⁶⁾(x)=-sin(x); f⁽⁶⁾(0)=0
f⁽⁷⁾(x)=-cos(x); f⁽⁷⁾(0)=-1
f⁽⁸⁾(x)=f⁽⁴⁾(x), f⁽⁹⁾(x)=f⁽⁵⁾(x), etc.
Series is x⁵/5!-x⁷/7!+x⁹/9!-...+(-1)ⁿx²ⁿ⁺⁵/(2n+5)! = ∑[n∈[0,∞)](-1)ⁿx²ⁿ⁺⁵/(2n+5)!