For any , vertical asymptotes occur at , where is an integer. Use the basic period for , , to find the vertical asymptotes for . Set the inside of the cotangent function, , for equal to to find where the vertical asymptote occurs for .

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Divide by .

Set the inside of the cotangent function equal to .

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

The basic period for will occur at , where and are vertical asymptotes.

The absolute value is the distance between a number and zero. The distance between and is .

The vertical asymptotes for occur at , , and every , where is an integer.

Cotangent only has vertical asymptotes.

No Horizontal Asymptotes

No Oblique Asymptotes

Vertical Asymptotes: where is an integer

Find the Asymptotes y=6cot(5x)