Answer
$tan\theta=\frac{y}{x}$ and $sec\theta=\frac{r}{x}$, $\cot\theta=\frac{x}{y}$ and $csc\theta=\frac{r}{y}$. $tan\theta=\frac{y}{x}$ and $\cot\theta=\frac{x}{y}$.
Work Step by Step
The trigonometric function will be undefined if the denominator is zero. Based on the definitions, we have $tan\theta=\frac{y}{x}$ and $sec\theta=\frac{r}{x}$. Thus these two functions will be undefined if $x=0$. Similarly, the functions that are undefined when $y=0$ are $\cot\theta=\frac{x}{y}$ and $csc\theta=\frac{r}{y}$. Among the trigonometric functions, there are two that do not depend on the value of $r$ and they are $tan\theta=\frac{y}{x}$ and $\cot\theta=\frac{x}{y}$.
