Question

Can someone please help me with this .. ASAP

Answer 1

Answer:
`(-5)/(4), (3)/(4)`

Explanation:

Given

`\theta` is in the third quadrant and

`\Rightarrow \cos \theta=(-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=-√(1-\cos^2 \theta)\\\Rightarrow \sin \theta =-\sqrt{1-(-(3)/(5)^2)}\\\Rightarrow \sin \theta =-(4)/(5)\\\Rightarrow\text{cosec} \theta=-(5)/(4)\\\Rightarrow \cot \theta=(\cos \theta)/(\sin \theta)=((-3)/(5))/((-4)/(5))=(3)/(4)`