**ERIC Number:**EJ992374

**Record Type:**Journal

**Publication Date:**2012

**Pages:**14

**Abstractor:**ERIC

**Reference Count:**12

**ISBN:**N/A

**ISSN:**ISSN-0819-4564

On Periodicity of Trigonometric Functions and Connections with Elementary Number Theoretic Ideas

Stupel, Moshe

Australian Senior Mathematics Journal, v26 n1 p50-63 2012

The notion of periodicity stands for regular recurrence of phenomena in a particular order in nature or in the actions of man, machine, etc. Many examples can be given from daily life featuring periodicity. Mathematically the meaning of periodicity is that some value recurs with a constant frequency. Students learn about the periodicity of the trigonometric functions--sine, cosine, tangent and cotangent, after they study the subject of extension of the trigonometric circle and the graphical representation of these functions. However, students encounter the notion of the period even before their studies in trigonometry. This article considers the properties of periodical functions, and how to find the period of the sum, the difference and the product functions of trigonometric functions. The author discusses the issue of the smallest period, and finds a connection between the period of a product of trigonometric functions and the period of their sum. A surprising connection between different mathematics topics is presented in the process of determining the period of the sum or product of trigonometric functions. (Contains 2 figures.)

Descriptors: Trigonometry, Arithmetic, Mathematical Formulas, Foreign Countries, Mathematics, Mathematics Curriculum, Definitions, Mathematical Logic, Validity, Mathematics Teachers

Australian Association of Mathematics Teachers (AAMT). GPO Box 1729, Adelaide 5001, South Australia. Tel: +61-8-8363-0288; Fax: +61-8-8362-9288; e-mail: office@aamt.edu.au; Web site: http://www.aamt.edu.au

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

**Education Level:**N/A

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A

**Identifiers - Location:**Australia