The cotangent function, represented as y = cot(x), has a specific period that is important for understanding how the function behaves when graphed.
The period of y = cot(x) is π (pi). This means that the function repeats its values every π units along the x-axis. In simpler terms, if you take any angle x, the cotangent of that angle will be the same as the cotangent of x + π.
To explain why this is the case, we can look at the cotangent function in terms of sine and cosine:
cot(x) = cos(x) / sin(x)
Since both sine and cosine functions have a period of 2π, when we observe cotangent, it effectively cancels out some of this periodicity. As we look at the behavior of cot(x) over the interval of 0 to 2π, we’ll see that it actually completes a full cycle and returns to its initial value just after π.
In summary, the cotangent function repeats its values every π radians, making the period of y = cot(x) equal to π.