The period of a trigonometric function, such as the cotangent, relates to how often the values of the function repeat. The usual period of a cotangent function is π. This gets modified when the function changes in certain ways.
In our specific function, y = 3cot(4x - 3pi), we can see that the x variable inside the cotangent function is being multiplied by a coefficient of 4. This affects the period of the function. Specifically, the period of our function will be the original period divided by the absolute value of the coefficient of x (which is 4 in this case).
To do this calculation, you would divide the original period (π) by the absolute value of the coefficient of x (4). So that would be:
```
π / 4
```
Performing this calculation gives you a numerical result. In decimal form, this result is approximately:
```
0.7853981633974483
```
So, the period of y= 3cot(4x-3pi) is approximately 0.7854.