Série de Maclaurin cos(x)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
Maclaurin cos
About this calculator
The Maclaurin series calculator for cos(x) approximates the cosine of an angle x (in radians) using the first terms of the series: cos x ≈ 1 − x²/2! + x⁴/4! − x⁶/6! + ... . You enter the value of x and the desired number of terms, and the tool computes the partial sum, displaying the approximate result. The formula uses factorials in the denominators, making manual calculation tedious for many terms; the calculator automates this process.
This tool is useful in numerical analysis, physics, and engineering contexts, where approximations of trigonometric functions are needed without scientific calculators. For example, when analyzing harmonic oscillations or Fourier series, the Maclaurin series expansion simplifies differential equations. Calculus students can verify the series convergence for different x values, observing how more terms improve accuracy.
Important considerations: the Maclaurin series for cos(x) converges for all real x, but the convergence rate depends on the value of x. For large |x|, many terms are needed for a good approximation. Also, the calculator uses rounding; check precision for critical applications. Remember that x must be in radians; if in degrees, convert by multiplying by π/180.
Frequently asked questions
How many terms should I use for a good approximation?
It depends on the value of x. For small |x| (e.g., 0.5), 3 or 4 terms already give good accuracy. For large |x| (e.g., 10), more than 10 terms are needed. The calculator lets you test different amounts.
Can I use degrees instead of radians?
No, the Maclaurin series requires x in radians. If you have an angle in degrees, convert to radians by multiplying by π/180 before using the calculator.
Does the series converge for all x?
Yes, the Maclaurin series for cos(x) converges for all real x. However, for very large values, convergence is slow and may require many terms.
What is the difference between Maclaurin series and Taylor series?
The Maclaurin series is a special case of the Taylor series, centered at x=0. For cos(x), both are equivalent when expanded around 0.
Is the result exact?
No, it is an approximation. The more terms you use, the closer the result is to the exact value (given by a scientific calculator). For applications requiring precision, use an adequate number of terms.