Question

Given cosθ=3/5 and 270°<θ<360° , find the exact value of each expression.

cotθ/2

Answer 1

`270^(\circ) < \theta < 360^(\circ) \implies 135^(\circ) < (\theta)/(2) < 180^(\circ) \implies \cot (\theta)/(2) < 0`

`\tan (\theta)/(2)=-\sqrt{(1-\cos \theta)/(1+\cos \theta)}=-\sqrt{(1-(3)/(5))/(1+(3)/(5))}=-(1)/(2)`

`\cot (\theta)/(2)=(1)/(\tan (\theta)/(2))=\boxed{-2}`