Question

If the function, f(x)=tan((x)/(4)), is periodic, what is its period?

Answer 1

The function f(x) = tan(x/4) has a period of 4π radians, as the basic period of the tangent function, which is π, is stretched by a factor of 4 due to the division by 4 inside the function.

Step-by-step explanation:

If we have a function f(x) = tan(x/4), the goal is to determine the period of this function. The tan function's period in its base form tan(x) is π, which means it repeats every π radians. To find the period of the given function, we need to account for the horizontal stretching caused by the division by 4 inside the function.

Steps to find the period:

1. Understand that the basic period of tan(x) is π radians.
2. Recognize that dividing x by a number stretches the function horizontally. In this case, dividing by 4 stretches it by a factor of 4.
3. Multiply the base period π by the stretch factor to find the new period: Period = π * 4 which is 4π radians.

Therefore, the function f(x) = tan(x/4) has a period of 4π radians.