Question

Determine whether the function tan(πx) is periodic. If so, find its fundamental period. If the function is not periodic, indicate that using the checkbox. The function is not periodic. T=

Answer 1

The function tan(πx) is periodic with a fundamental period of T = 1.

Step-by-step explanation:

The function tan(πx) is indeed periodic. To find the fundamental period of this function, we need to consider the properties of the tangent function. The standard tangent function, tan(x), has a period of π. This means that it repeats its values every π radians. When we have tan(πx), the π inside the function argument effectively compresses the x-axis by a factor of π, which causes the function to complete one cycle when x has increased by 1 (because π times 1 is π).

Therefore, the function tan(πx) has a period of T = 1, because tan(π(x + 1)) = tan(πx + π) is the same as tan(πx), due to the periodicity of the tangent function.