blackscorpion said:That certainly works since the difference in sin(x) and your T(x)with your x value is 9.16x10^-6
How did you get this answer?
The purpose of finding the value of h for Sin(x) approximation is to calculate an approximate value for the sine function at a specific angle x. This is useful in various mathematical and scientific applications, such as graphing and solving equations involving trigonometric functions.
The value of h for Sin(x) approximation is determined using the Taylor series expansion of the sine function. This series involves an infinite sum of terms, but by choosing an appropriate value for h, we can approximate the function with a finite number of terms, providing a close approximation to the actual value.
The value of h in the Taylor series expansion is known as the step size or interval. It determines the distance between each term in the series and ultimately affects the accuracy of the approximation. A smaller h value will result in a more accurate approximation, but it also requires more computations.
No, the value of h cannot be negative in Sin(x) approximation. The Taylor series expansion is based on positive powers of h, and a negative value would result in negative powers, which would not accurately approximate the sine function.
Yes, there is a formula for finding the value of h for Sin(x) approximation, known as the "h-formula." It is h = (2n + 1)π /2, where n is the number of terms used in the approximation. This formula provides a good starting point for finding the optimal value of h, but it may need to be adjusted for different values of x or for increased accuracy.