Thus, the Maclaurin series for sin(x) is Step 3: Write the Expansion in Sigma Notation. From the first few terms that we have calculated, we can see a pattern that allows us to derive an expansion for the n th term in the series, which is Substituting this into the formula for the Taylor series expansion, we obtain Radius of Convergence.
Depending on its arguments, sin returns floating-point or exact symbolic results. Compute the sine function for these numbers. Because these numbers are not symbolic objects, sin returns floating-point results. Compute the sine function for the numbers converted to symbolic objects. For many symbolic (exact) numbers, sin returns unresolved.
More generally, the definition of sine (and other trigonometric functions) can be extended to any real value in terms of the length of a certain line segment in a unit circle.More modern definitions express the sine as an infinite series or as the solution of certain differential equations, allowing their extension to arbitrary positive and negative values and even to complex numbers.