where does the graph of the function y = tan(x) have asymptotes? at the values of x where cos(x)=0 at the…

where does the graph of the function y = tan(x) have asymptotes? at the values of x where cos(x)=0 at the values of x where sin(x)=0 at the values of x where cos(x) is undefined at the values of x where sin(x) is undefined

where does the graph of the function y = tan(x) have asymptotes? at the values of x where cos(x)=0 at the values of x where sin(x)=0 at the values of x where cos(x) is undefined at the values of x where sin(x) is undefined

Answer

Explanation:

Step1: Recall tangent - cosine relationship

The tangent function is defined as $\tan(x)=\frac{\sin(x)}{\cos(x)}$.

Step2: Determine asymptote condition

A rational function $y = \frac{f(x)}{g(x)}$ has asymptotes where $g(x)=0$. For $y = \tan(x)=\frac{\sin(x)}{\cos(x)}$, it has asymptotes when $\cos(x)=0$.

Answer:

at the values of x where $\cos(x)=0$