Sketching the arccot function involves determining its basic shape, key characteristics, and asymptotic behavior. The arccot function, denoted as arccot(x), is the inverse function of the cotangent function. It represents the angle whose cotangent is x.
To sketch the graph, start by plotting a few key points. The arccot function has vertical asymptotes at x = /2, where the cotangent function has zeros. The graph approaches these asymptotes as x approaches . The arccot function is also an odd function, meaning that arccot(-x) = -arccot(x). This symmetry implies that the graph is symmetric about the origin.
