Question

How do you find the asymptotes for `f(x)=tan2x`?

Answer 1

Recall that `y = tanx` can be written as `y = sinx/cosx`. Then there will be asymptotes whenever `cosx = 0`, since we cannot have the denominator equal `0` without making the function undefined in the real number system.

Similarly, `f(x) = tan2x` can be rewritten as `f(x) = (sin2x)/(cos2x)`. We need to find the values of `x` that make `cos2x= 0`.

`cos2x= 0`

`2x = arccos(0)`

`2x = pi/2, (3pi)/2`

`x = pi/4 and (3pi)/4`

Don't forget to add the periodicity. The function `y = cos2x` has a period of `pi`, so there will be asymptotes in `tan(2x)` whenever `x= pi/4 + pin` or `x = (3pi)/4 + pin`, where `n` is an integer.

Hopefully this helps!