Find the Range y=cot(x)

Problem

y=cot(x)

Solution

1. Identify the definition of the cotangent function in terms of sine and cosine.

cot(x)=cos(x)/sin(x)

2. Analyze the behavior of the function as x approaches the vertical asymptotes, which occur where sin(x)=0 (at x=n*π for any integer n.

(lim_x→0)(cot(x))=∞

(lim_x→π−)(cot(x))=−∞

3. Observe that the cotangent function is continuous on every open interval (n*π,(n+1)*π) Since the function goes from negative infinity to positive infinity within each period, it takes on every possible real value.

4. Determine the range based on the output values. The output y can be any real number.

Final Answer

Range of *y=cot(x)* is *(−∞,∞)

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