Question

Can someone please help me with this .. ASAP

Answer 1

Answer:$\frac{-5}{4}, \frac{3}{4}$

Step-by-step explanation:

Given

$\theta$ is in the third quadrant and

$\Rightarrow \cos \theta=\frac{-3}{5}$

tan and cot is positive in the third quadrant and the rest are negative

using identity

$\sin^2 \theta+\cos^2 \theta=1\\\Rightarrow \sin \theta=-\sqrt{1-\cos^2 \theta}\\\Rightarrow \sin \theta =-\sqrt{1-(-\frac{3}{5}^2)}\\\Rightarrow \sin \theta =-\frac{4}{5}\\\Rightarrow\text{cosec} \theta=-\frac{5}{4}\\\Rightarrow \cot \theta=\frac{\cos \theta}{\sin \theta}=\frac{\frac{-3}{5}}{\frac{-4}{5}}=\frac{3}{4}$