For what value of theta is the fraction 1/tan of theta undefined?Please explain this, I am so so confused.

Expert Answers
hala718 eNotes educator| Certified Educator

Let `y= 1/tantheta `

We need to find the values of `theta`  such that the function (y) is defined.

Since `tan(theta)`  is in the denominator, then we know that `tan(theta)`  can not be 0.

==> `tantheta != 0`

Now we will find the values where `tan(theta)= 0`  and exclude them from the domain.

`==gt tan(theta)= 0 `

`==gt (sintheta)/(costheta)= 0 `

`==gt sin(theta)= 0 `

`==gt theta = 2npi` (n= 0, 1, 2, ...)

==> Then `1/(tantheta)`  is not defined when `theta= 2npi`  (n= 0, 1, 2..)