Answer
$\sin{\theta} =\dfrac{1}{a}$
$\cos{\theta} =\dfrac{\sqrt{a^2-1}}{a}$
$\tan{\theta} = \dfrac{1}{\sqrt{a^2-1}}$
$\csc{\theta} = a$
$\sec{\theta} =\dfrac{a}{\sqrt{a^2-1}}$
$\cot{\theta} =\sqrt{a^2-1} $
Work Step by Step
$\csc{\theta} = a$
$\sin{\theta} = \dfrac{1}{\csc{\theta}} = \dfrac{1}{a}$
$\because \theta \in QI \hspace{20pt} \therefore \cos{\theta}$ is positive.
$\cos{\theta} = \sqrt{1-\sin^2{\theta}} = - \sqrt{1-\left(\dfrac{1}{a}\right)^2} = \sqrt{\dfrac{a^2-1}{a^2}} = \dfrac{\sqrt{a^2-1}}{a}$
$\tan{\theta} = \dfrac{\sin{\theta}}{\cos{\theta}} = \dfrac{1}{\sqrt{a^2-1}}$
$\sec{\theta} = \dfrac{1}{\cos{\theta}} = \dfrac{a}{\sqrt{a^2-1}}$
$\cot{\theta} = \dfrac{1}{\tan{\theta}}= \sqrt{a^2-1} $
