SUMMARY
The function f(x) = cos^2(x) + sin^2(x) is not a periodic function. While both cos^2(x) and sin^2(x) are periodic, their sum equals 1, which is a constant function. A function is defined as periodic if there exists a smallest positive integer P≠0 such that f(x+P) = f(x). In this case, since f(x) = 1 for all x, there is no smallest period, confirming that it is not periodic.
PREREQUISITES
- Understanding of periodic functions
- Knowledge of trigonometric identities, specifically sin^2(x) + cos^2(x) = 1
- Familiarity with the definition of fundamental frequency
- Basic concepts of function behavior in mathematics
NEXT STEPS
- Study the properties of periodic functions in detail
- Explore the implications of constant functions in mathematical analysis
- Learn about the concept of fundamental period in trigonometric functions
- Investigate other trigonometric identities and their periodicity
USEFUL FOR
Students of mathematics, particularly those studying trigonometry and function analysis, as well as educators seeking to clarify concepts of periodicity in functions.