The functions are and .

Consider .

Let  , then .

The trigonometric function : .

.

Pythagorean theorem : .

.

The trigonometric function : .

.

The functions are equal.

Find the asymptotes of .

Find the vertical asymptotes by solving zeros of denominator. \ \

Since the roots are imaginary,  there is no vertical asymptotes. 

To find horizontal asymptote, first find the degree of the numerator and  the degree of denominator.

Degree of the numerator and the degree of denominator.

Since the degree of the numerator is equal to the degree of the denominator, horizontal asymptote is the ratio of the leading coefficient of numerator and denominator.

Leading coefficient of numerator , leading coefficient of denominator

.

Horizontal asymptotes are .

Graph of or is :

Graph of or is :

Horizontal asymptotes are .