Taylor series question: some the coefficients of the powers of x in the Taylor polynomial for the function f(x) = tan(x) are 0. What property of the function tan(x) does this reflect?

Question

anonymous · Answer

first three terms:
$$x^{1} + \frac{1}{3}x^{3} +\frac{2}{15}x^{5}$$

hartnn · Answer

hint:
Foe even functions, f(x) = f(-x)
for odd functions , f(x)= -f(-x)
so what u think? tan is even or odd ?

anonymous · Answer

odd

hartnn · Answer

thats correct if that what u wanted..............................

anonymous · Answer

so it reflects its odd property that all the even powers of x have 0 as a coefficient

hartnn · Answer

yes,i think so , that why even powers are missing