# How would I go about finding the vertical and horizantal asymtotes (if any) of the function f(x)=cscðx?

Thanks for all your help.

Corin

## change the function to 1/sinTheta.

Now: Horizontal Asy...when i the numerator zero? Ans: never

Vertical Asy..When is the denominator zero? Ans: At multiples of Theta equal to 180 (0, 180, 360, ..).

change the function to 1/sinTheta.

Now: Horizontal Asy...when i the numerator zero? Ans: never

Vertical Asy..When is the denominator zero? Ans: At multiples of Theta equal to 180 (0, 180, 360, ..).

## So I would write the Vertical Asy answer...

x=0+(pi)n

correct?

since 180=pi and it can be added "n" number of times

please let me know if this is the correct notation

thanks so much for your help

--Corin

## Yes, correct. I would have done it this way..

n*PI n=0,1,2,3,...

## To find the vertical and horizontal asymptotes of the function f(x) = csc(x), we can follow these steps:

1. Vertical Asymptotes:

Vertical asymptotes occur when the function approaches infinity or negative infinity as x approaches a certain value. For csc(x), vertical asymptotes occur where the function becomes undefined, which happens when the sine function is equal to zero (since csc(x) is the reciprocal of sin(x)).

So, to find the vertical asymptotes, we need to determine the values of x for which sin(x) = 0. In the case of sin(x), this happens when x is an integer multiple of π (pi), such as x = π, 2π, -π, -2π, and so on. Therefore, the vertical asymptotes of f(x) = csc(x) are x = nπ, where n is an integer.

2. Horizontal Asymptotes:

Horizontal asymptotes occur when the function approaches a certain value as x approaches positive or negative infinity. For csc(x), there is no horizontal asymptote because the function oscillates between positive and negative infinity as x approaches infinity or negative infinity.

In summary, the vertical asymptotes of f(x) = csc(x) are x = nπ, where n is an integer, and there are no horizontal asymptotes.