You could determine this term to begin.by using the next nonvanishing term of the Taylor series
If the real value is 0.5 and the approximation is 0.45 (arbitrary numbers), what is the relative deviation?How do I calculate the accuracy ?
engboysclub said:I'm not really sure - I know what Taylor series is - Graphically and what it does but I don't know how to implement it or work it out.
The Taylor Series for approximating sin(x) is:
sin(x) = x - (x^3)/3! + (x^5)/5! - (x^7)/7! + ...
The accuracy of the Taylor Series approximation for sin(x) depends on the number of terms used in the series. The more terms used, the more accurate the approximation will be. However, since the series is an infinite sum, it will never be an exact match for the actual sin(x) function.
The number of terms needed for accurate approximation varies depending on the desired level of accuracy. Generally, using more terms will result in a more accurate approximation, but it is also important to consider the computational time and resources required for calculating a larger number of terms.
The Maclaurin Series is a special case of the Taylor Series where the center of the series is at x=0. It is the Taylor Series at x=0 for a given function. Therefore, the Maclaurin Series for sin(x) is simply:
sin(x) = x - (x^3)/3! + (x^5)/5! - (x^7)/7! + ...
The Taylor Series approximation for sin(x) can be improved by using more terms in the series or by using a different approximation method, such as using a more accurate formula for calculating the coefficients. Additionally, using a smaller interval for x values can also improve the accuracy of the approximation.