The vertical asymptotes for the function y = 6 tan(0.2x) are found by determining the values of x where the function becomes infinitely large or infinitely small.
In the case of the tangent function, the vertical asymptotes occur when the argument of the tangent function (0.2x in this case) is equal to an odd multiple of pi/2, since that is when the tangent function becomes undefined.
So we can find the vertical asymptotes by solving the equation:
0.2x = (2n + 1) * pi/2
where n is an integer. Solving for x, we get:
x = (2n + 1) * pi / (2 * 0.2) = 5 * (2n + 1) * pi/2
So the vertical asymptotes occur at x = 5 * pi/2, x = 11 * pi/2, x = 17 * pi/2, and so on.
Note that these are not the only vertical asymptotes, since the function y = 6 tan(0.2x) is periodic with a period of 2 * pi / 0.2, which is much larger than pi. The function will have additional vertical asymptotes at the same values plus or minus 2 * pi / 0.2, and so on.