Specify the smallest positive period of the function y = 1 / 3ctg (1 / 2x + 3)

Find the smallest positive period of the function y = 1/3 * ctg (1/2 * x + 3).
The period is found by the formula T1 = T / | k | functions y = A * f (k * x + b), where A = 1/3, k = 1/2 and b = 3. The function ctg is odd and has a period T = pi. Then we get:
T1 = T / | k | = pi / | 1/2 | = pi / (1/2) = pi * 2/1 = pi * 2 = 2 * pi;
Answer: The smallest positive period is T = 2 * pi.