Question

How do you find the vertical, horizontal or slant asymptotes for `y= cot (x/2)`?

Answer 1

You know that `cot(theta) = 1/tan(theta) = cos(theta)/sin(theta)`

and you know that this will be undefined wherever the value of the denominator is zero - because you can't divide by zero.

`sin(theta) = 0` when `theta = 0,pi,2pi,3pi...`

so, if `x/2 = theta`, then, we have a vertical asymptote when

`x/2 = 0,pi,2pi,3pi...`

multiply the left side (and every item in the sequence on the right side) by 2 gives us:

`x = 0, 2pi, 4pi, 6pi...`