Enter a problem...
Calculus Examples
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 tangent function, , for equal to to find where the vertical asymptote occurs for .
Divide each term in by .
Simplify the left side.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify the right side.
Multiply the numerator by the reciprocal of the denominator.
Cancel the common factor of .
Move the leading negative in into the numerator.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
Set the inside of the tangent function equal to .
Divide each term in by .
Simplify the left side.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify the right side.
Multiply the numerator by the reciprocal of the denominator.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
The basic period for will occur at , where and are vertical asymptotes.
is approximately which is positive so remove the absolute value
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
The vertical asymptotes for occur at , , and every , where is an integer.
Tangent only has vertical asymptotes.
No Horizontal Asymptotes
No Oblique Asymptotes
Vertical Asymptotes: where is an integer