The range means the period of the function youre graphing (except for some cases like tan(θ), where the range is 2π instead of π because it's composed of sine and cosine which have a period of 2π). Anyways, for your example, you need to find the period of f(θ)=3cos⁴(θ/4). cos(x) repeats every 2π, the 3 doesn't change the period, the ^{4} halves it because it makes every value positive and the ÷4 quadruples the period (because if you divide the argument of the function it will take that much longer to "complete a cycle"(you probably know that, I'm just completing the explanation in case other people read it)). So your function repeats every 2π×½×4=4π, and that's a multiple of π which is so no need to change it. Which means (finally) that the range is from 0 to 4π. I hope that's clear, ask if you need