**ERIC Number:**EJ926375

**Record Type:**Journal

**Publication Date:**2011-May

**Pages:**7

**Abstractor:**ERIC

**ISBN:**N/A

**ISSN:**ISSN-0025-5769

**EISSN:**N/A

Exposing the Mathematical Wizard: Approximating Trigonometric Functions

Gordon, Sheldon P.

Mathematics Teacher, v104 n9 p676-682 May 2011

For almost all students, what happens when they push buttons on their calculators is essentially magic, and the techniques used are seemingly pure wizardry. In this article, the author draws back the curtain to expose some of the mathematics behind computational wizardry and introduces some fundamental ideas that are accessible to precalculus students and that inspire many of them to pursue mathematics. In the process, he shows how these ideas provide a wonderful opportunity to make connections between seemingly disparate mathematical threads--such as use of data analysis and trigonometric identities and the behavior of polynomials and sines and cosines--to link them and provide teachers with new ways to reinforce important concepts and methods. All that a calculator can do is addition and subtraction; thus, "every" other operation--multiplication, taking the square root, and so on--necessarily involves some very clever numerical scheme. The author considers the problem of how one approximates a function, typically a transcendental function such as the sine or the cosine, with a simpler function, usually a polynomial, to calculate values of the function. (Contains 14 figures and 3 tables.)

Descriptors: Data Analysis, Geometric Concepts, Trigonometry, Calculus, Mathematics Instruction, Algebra, Mathematical Formulas, Calculators, Mathematics Education, Mathematics, Intervals

National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191-1502. Tel: 800-235-7566; Tel: 703-620-3702; Fax: 703-476-2970; e-mail: orders@nctm.org; Web site: http://www.nctm.org/publications/

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**N/A

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A

**Grant or Contract Numbers:**N/A