# How do you write 5th degree taylor polynomial for sin(x)?

With both x and a in radian measure,

Taylor expansion is about a neighboring point x = a, in contrast to

Maclaurin's that is about x = 0.

The expansion is

f(x) f(a) +(x-a)f'(a)+(x-a)^2/(2!)f''(a)+(x-a)^3/(3!)f'''(a)+.... Accordingly, here

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The fifth-degree Taylor polynomial for sin(x) is given by:

[ P_5(x) = x - \frac{x^3}{3!} + \frac{x^5}{5!} ]

This polynomial approximates the function sin(x) near the point x = 0 up to the fifth-degree term.

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