Question 1 Find the values of the trigonometric functions of $t$ if cost $=-\frac{3}{5}$ and the terminal point of $t$ is in quadrant III. a. $\sin t=-\frac{4}{5}, \cos t=-\frac{3}{5}, \tan t=\frac{4}{3}, \cot t=\frac{3}{4}$ b. $\sin t=-\frac{4}{5}, \cos t=-\frac{3}{5}, \tan t=-\frac{4}{3}, \cot t=-\frac{3}{4}$ c. $\sin t=\frac{4}{5}, \cos t=-\frac{3}{5}, \tan t=\frac{4}{3}, \cot t=\frac{3}{4}$

Step 1 ：Given that \(\cos t = -\frac{3}{5}\) and the terminal point of \(t\) is in quadrant III.

Step 2 ：In the third quadrant, both sine and cosine are negative. Since we know that \(\cos t = -\frac{3}{5}\), we can use the Pythagorean identity \(\sin^2 t + \cos^2 t = 1\) to find \(\sin t\).

Step 3 ：\(\sin t = -\sqrt{1 - \cos^2 t} = -\sqrt{1 - \left(-\frac{3}{5}\right)^2} = -\frac{4}{5}\)

Step 4 ：We can then use the definitions of tangent and cotangent in terms of sine and cosine to find the values of \(\tan t\) and \(\cot t\).

Step 5 ：\(\tan t = \frac{\sin t}{\cos t} = \frac{-4/5}{-3/5} = \frac{4}{3}\)

Step 6 ：\(\cot t = \frac{1}{\tan t} = \frac{3}{4}\)

Step 7 ：Final Answer: \(\boxed{\sin t=-\frac{4}{5}, \cos t=-\frac{3}{5}, \tan t=\frac{4}{3}, \cot t=\frac{3}{4}}\)