Answer
$$\sin t = - \frac{4}{5}, \quad \cos t = -\frac{3}{5}, \\ \tan t =\frac{4}{3}, \quad \cot t=\frac{3}{4}, \\ \sec t = -\frac{5}{3}, \quad \csc t =- \frac{5}{4}$$
Work Step by Step
According to the information given in the question, for the point $P$ we have$$x=-\frac{3}{5}, \quad y= - \frac{4}{5}, \quad r=1.$$ So we can find the value of the trigonometric functions as follows.$$\sin t =\frac{y}{r}=\frac{-\frac{4}{5}}{1}=-\frac{4}{5}, \quad \cos t =\frac{x}{r}=\frac{-\frac{3}{5}}{1}=-\frac{3}{5}, \\ \tan t =\frac{y}{x}=\frac{-\frac{4}{5}}{-\frac{3}{5}}=\frac{4}{3}, \quad \cot t =\frac{x}{y}=\frac{-\frac{3}{5}}{-\frac{4}{5}}=\frac{3}{4}, \\ \sec t =\frac{r}{x}=\frac{1}{-\frac{3}{5}}=-\frac{5}{3}, \quad \csc t =\frac{r}{y}=\frac{1}{-\frac{4}{5}}=-\frac{5}{4}$$
