Find the x and y Intercepts y=cot(x)

Problem

y=cot(x)

Solution

1. Identify the condition for the y-intercept by setting x=0

2. Evaluate the function at x=0 Since cot(x)=cos(x)/sin(x) we check the value of sin(0)

3. Determine that because sin(0)=0 the expression cos(0)/sin(0)=1/0 is undefined. Therefore, there is no y-intercept.

4. Identify the condition for the x-intercepts by setting y=0

5. Solve the equation cot(x)=0 which occurs when cos(x)=0 and sin(x)≠0

6. Find the general solution for cos(x)=0 which is x=π/2+n*π for any integer n

Final Answer

x-intercepts: *x=π/2+n*π, y-intercept: None

Want more problems? Check here!