Graph y=-cot(x)

Problem

y=−cot(x)

Solution

1. Identify the parent function and its properties. The parent function is y=cot(x) which has vertical asymptotes where sin(x)=0 specifically at x=n*π for any integer n

2. Determine the effect of the negative sign, which represents a reflection across the xaxis. While the standard cotangent function decreases on every interval of its domain, the reflected function y=−cot(x) increases on every interval.

3. Locate the x-intercepts by finding where cot(x)=0 This occurs where cos(x)=0 which is at x=π/2+n*π

4. Identify key points for one period between the asymptotes x=0 and x=π At x=π/4 y=−cot(π/4)=−1 At x=(3*π)/4 y=−cot((3*π)/4)=1

5. Sketch the graph by drawing the vertical asymptotes at x=0,±π,±2*π,… and plotting the increasing curves through the intercepts and key points.

Final Answer

y=−cot(x)

Want more problems? Check here!