Question

Find a cotangent function with x-intercepts at 5π and -5π and

vertical asymptotes at 5π/2 and -5π/2,

Answer 1

To find a cotangent function with x-intercepts at 5π and -5π and vertical asymptotes at 5π/2 and -5π/2, we can start by finding the tangent function with the given properties and then take the reciprocal to get the cotangent function.

Step-by-step explanation:

To find a cotangent function with x-intercepts at 5π and -5π and vertical asymptotes at 5π/2 and -5π/2, we need to consider the properties of the cotangent function. Cotangent is the reciprocal of tangent, so we can start by finding the tangent function with the given properties.

The tangent function has x-intercepts at π and -π, and vertical asymptotes at π/2 and -π/2. We can express the tangent function with these properties as tan(x) = A(sec(x) - 1), where A is a constant.

Now, to find the cotangent function, we take the reciprocal of tangent: cot(x) = 1/tan(x). Substituting our expression for tangent, we get cot(x) = 1/(A(sec(x) - 1)). This is the desired cotangent function.