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I would like to know if the Taylor series for the sine function,

$$\sin{x} = x -\frac{x^3}{3!} + \frac{x^5}{5!} - \cdots,$$

is convergent if the argument of the function, $x$, is expressed in degrees instead of radians.

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Er... if you use the series, the $x$ is supposed to be in radians. If you want to use degrees, then you need the extra factor of $\pi/180$... –  J. M. Nov 20 '11 at 15:02
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If you mean to use $x=30$ instead of $x=\frac{\pi}{6}$, then it would converge, but not to the value of sine of 30 degrees. –  Sasha Nov 20 '11 at 15:33
    
@J.M.: Thank you for your comment. As you suggest, if I want to use degrees, then I should make a variable change, true? –  jufrpeji Nov 20 '11 at 15:39
    
@Sasha: Thank you for your explanation. I think I have just understood it now. –  jufrpeji Nov 20 '11 at 15:43

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