Your question does not make sense. You are making a trigonometric function into an infinite polynomial. Why would you expect any visual similarity?
Besides the sign error on the 3rd derivative, you have it.
hey guys ive attached a jpg with the question:
f(x)= sin3x
f'(x)= 3cos3x
f''(x) = -3.3sin3x
f'''(x) = 3.3.3cos3x
I took a=0 and began to input it into the derivations:
f(0) = 0
f'(0) = 3
f''(0) = 0
f''' (0) = 27
but when i put it into the maclaurin series i get 3x + 27x^3/3!
shudnt i get the original formula again? what have i done wrong?