Answer
$f(x) = x - \frac{1}{3!}x^{3} + \frac{1}{5!}x^{5}$
Work Step by Step
$f(x) = sin (x)$
$f(x) = f(0) + f^{1}(0)x + \frac{f^{''}(0)}{2!}x^{2} + \frac{f^{'''}(0)}{3!}x^{3} + ... + \frac{f^{n}(0)}{n!}x^{n}$
$f(0) = sin (0) = 0$
$f'(0) = cos (0) = 1$
$f''(0) = -sin (0) = 0$
$f'''(0) = -cos (0) = -1$
$f''''(0) = sin (0) = 0$
$f'''''(0) = cos (0) = 1$
Maclaurin polynomial for $n=5$ is
$f(x) = x - \frac{1}{3!}x^{3} + \frac{1}{5!}x^{5}$
