sin(x) and cos(x) have fundamental period 2pi; tan(x) and cot(x) have period pi. For f(x) = Asin(Bx + C) + D: amplitude = |A|, period = 2pi/|B|, phase shift = -C/B, vertical shift = D. The period of |sin(x)| = pi, and $sin^2$(x) = pi. For combinations like sin(2x) + cos(3x), the period is the LCM of individual periods (pi and 2pi/3, so LCM = 2*pi). Note: LCM may not exist if the ratio of periods is irrational (e.g., sin(x) + sin(sqrt(2)*x) is not periodic). Understanding periodicity helps in counting solutions in an interval.