Approximations of Sine



This applet shows the Sine function and three approximations for the Sine function.
  • An early approximation for sine was from Bhaskara I is . This function is fairly accurate for angles between .
  • Another approximation is a power series (MacLaurin or Taylor Series) which for the Sine function is . The number of terms can be increased to obtain any desired accuracy.
The third approximation is a product series used in the calculation of .
  • Since the Sine function is zero at it can be approximated as . This is the Root Products Approximation.
  • Polynomial Interpolation that go through a set of points. Two points define a line. For more points the polynomial can be defined as using Lagrange Polynomials. Note, the value of the product is zero at all points and one when .
Compare the different approximations as extra terms are added. How many terms are required for the MacLaurin Series to achieve grater accuracy than the other approximations? Where do the approximations provide more accurate values?