SUMMARY
The domain of the function tan(x/b) is all real numbers except for odd multiples of bπ/2. This conclusion is drawn from the properties of the tangent function, which is undefined at x = ±(2n+1)π/2 for any integer n. The correct representation of the domain can be expressed as D = { x | x ≠ b(π/2 + nπ), n ∈ ℤ }. The discussion clarifies that the teacher's assertion of the domain being solely bn(π/2) is incorrect.
PREREQUISITES
- Understanding of trigonometric functions, specifically the tangent function.
- Familiarity with the concept of domain in mathematics.
- Knowledge of integer sets and their notation (e.g., ℤ).
- Basic graphing skills for trigonometric functions.
NEXT STEPS
- Study the properties of the tangent function and its asymptotes.
- Learn about the transformations of trigonometric functions, including vertical and horizontal stretches.
- Explore the implications of changing the variable in trigonometric functions, such as tan(kx).
- Investigate the graphical representation of tan(x/b) and its domain visually.
USEFUL FOR
Students studying trigonometry, mathematics educators, and anyone seeking to understand the behavior of the tangent function and its transformations.