Explore the fascinating world of trigonometric power series with our advanced online calculator. Easily approximate values for sine and cosine functions using Taylor and Maclaurin series expansions, understand convergence, and analyze the impact of the number of terms. Perfect for students and engineers needing precise mathematical tools.
Formula:
The Taylor/Maclaurin series expands trigonometric functions into an infinite sum of terms. Our calculator approximates these series up to N terms.
For Sine (sin(x)):
sin(x) = x - x3⁄3! + x5⁄5! - x7⁄7! + ...
Or, generally: ∑n=0N-1 ((-1)n · x(2n+1)) ⁄ (2n+1)!
For Cosine (cos(x)):
cos(x) = 1 - x2⁄2! + x4⁄4! - x6⁄6! + ...
Or, generally: ∑n=0N-1 ((-1)n · x(2n)) ⁄ (2n)!
Where:
x = Angle in radians
N = Number of terms to include in the approximation (the summation runs from n=0 to N-1 for N terms).