Answer:[tex]\frac{-5}{4}, \frac{3}{4}[/tex]
Step-by-step explanation:
Given
[tex]\theta[/tex] is in the third quadrant and
[tex]\Rightarrow \cos \theta=\frac{-3}{5}[/tex]
tan and cot is positive in the third quadrant and the rest are negative
using identity
[tex]\sin^2 \theta+\cos^2 \theta=1\\\Rightarrow \sin \theta=-\sqrt{1-\cos^2 \theta}\\\Rightarrow \sin \theta =-\sqrt{1-(-\frac{3}{5}^2)}\\\Rightarrow \sin \theta =-\frac{4}{5}\\\Rightarrow\text{cosec} \theta=-\frac{5}{4}\\\Rightarrow \cot \theta=\frac{\cos \theta}{\sin \theta}=\frac{\frac{-3}{5}}{\frac{-4}{5}}=\frac{3}{4}[/tex]
