Find the Maclaurin series for f(x)=sin(x)f(x) = \sin(x)f(x)=sin(x) (first four non-zero terms).
x−x33!+x55!−x77!+⋯x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \cdotsx−3!x3+5!x5−7!x7+⋯
x−x36+x5120−x75040+⋯x - \frac{x^3}{6} + \frac{x^5}{120} - \frac{x^7}{5040} + \cdotsx−6x3+120x5−5040x7+⋯
1−x22!+x44!−x66!+⋯1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!} + \cdots1−2!x2+4!x4−6!x6+⋯
x−x32+x524−x7720+⋯x - \frac{x^3}{2} + \frac{x^5}{24} - \frac{x^7}{720} + \cdotsx−2x3+24x5−720x7+⋯