Taylor Series Approximation to Cosine

If a function has a Taylor series that is convergent to the function, it is customary to expect that partial sums with more terms provide a better approximation than those with fewer terms. As the example of y = cos(x) shows, this statement must be qualified.

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Minimum and maximum values on the axes that define the view frame are clickable and also respond to the cursor being dragged in their vicinity. To increase a number, click or drag the cursor a little to the right of the central line of the number. To decrease it, click or drag to the left from the central line.

For x large in absolute value, higher degree polynomials provide worse approximation than lower degree polynomials. For such x, the best approximation is given by the constant term y = 1.

• What Is Line?
• Functions, what are they?
• Cartesian Coordinate System
• Addition and Subtraction of Functions
• Function, Derivative and Integral
• Graph of a Polynomial of arbitrary degree
• Graph of a Polynomial Defined by Its Roots
• Inflection Points of Fourth Degree Polynomials
• Lagrange Interpolation (an Interactive Gizmo)
• Equations of a Straight Line
• Linear Function with Coefficients in Arithmetic Progression
• Sine And Cosine Are Continuous Functions