Convergence of the Taylor series for the sine function
I would like to know if the Taylor series for the sine function,
sin(x) = x - x^3/3! + x^5/5! -...
is convergent if the argument of the function, x , is expressed in degrees instead of radians.
Re: Convergence of the Taylor series for the sine function
Well wouldn't that imply that one degree equals one radian?!?
Re: Convergence of the Taylor series for the sine function
Quote:
Originally Posted by
jfpeji
I would like to know if the Taylor series for the sine function,
sin(x) = x - x^3/3! + x^5/5! -...
is convergent if the argument of the function, $x$, is expressed in degrees instead of radians.
That series converges for arbitrary complex
, to
where in the
the argument is to be regarded as in radians.
A different series converges to the sin where the argument is in degrees
CB
Re: Convergence of the Taylor series for the sine function
Ok. You are right. Thank you for your answer.
Re: Convergence of the Taylor series for the sine function
What is that different series which converges to the sin, where the argument is in degrees, that you mention?
Re: Convergence of the Taylor series for the sine function
Quote:
Originally Posted by
jfpeji
What is that different series which converges to the sin, where the argument is in degrees, that you mention?
The rather obvious:
=\left(\frac{\pi}{180}\right)x- \left(\frac{\pi}{180}\right)^3\frac{x^3}{3!}+\left (\frac{\pi}{180}\right)^5\frac{x^5}{5!}- ...)
CB
Re: Convergence of the Taylor series for the sine function
Ok. You are right. Thank you for your answer.