determine the period y= -3 tan(3x+pi)+2
The function y repeats when 3x increases by 2 pi. That makes the "period" 2 pi/3.
Your y function does not contain a "time" term, t. You are really asking for a wavelength
actually, tan(x) has period pi.
To determine the period of the function y = -3 tan(3x+π) + 2, we need to understand a few key concepts.
The tangent function, tan(x), is a periodic function with a period of π. This means that the graph of y = tan(x) repeats itself every π units.
However, your function has an additional factor of 3 inside the argument of the tangent function, which means the period will be affected. To find the period of the modified function, we need to divide the original period of the tangent function (which is π) by the coefficient of x inside the parentheses.
In this case, the coefficient is 3. So, the period of the y = -3 tan(3x+π) function will be the original period (π) divided by 3, giving us a period of π/3.
Therefore, the period of the given function y = -3 tan(3x+π) + 2 is π/3.