Answer
Required trigonometric functions are-
$\sin A = \frac{1}{\sqrt 6}$
$\\csc A = \sqrt 6$
$\\cos A = \frac{\sqrt 5}{\sqrt 6}$
$\\sec A = \frac{\sqrt 6}{\sqrt 5}$
$\\tan A = \frac{1}{\sqrt 5}$
$\\\cot A = \sqrt 5 $
Work Step by Step
Steps to Answer-
From the given diagram of triangle ABC, we will use given information and Pythagoras Theorem to solve for 'c'-
$c^{2} =a^{2} + b^{2}$ ( Pythagoras Theorem)
$c^{2} = 1^{2} + (\sqrt 5)^{2}$
$c^{2} = 1 + 5$
$c^{2} = 6$
therefore $ c = \sqrt 6$
Now we can write the required six T-functions of A using a = 1, $b= \sqrt5$ and c =$ \sqrt6$
$\sin A = \frac{a}{c} = \frac{1}{\sqrt 6}$
$\\csc A = \frac{c}{a} = \frac{\sqrt 6}{1} = \sqrt 6$
$\\cos A = \frac{b}{c} = \frac{\sqrt 5}{\sqrt 6}$
$\\sec A = \frac{c}{b} = \frac{\sqrt 6}{\sqrt 5}$
$\\tan A = \frac{a}{b} = \frac{1}{\sqrt 5}$
$\\\cot A = \frac{b}{a} = \frac{\sqrt 5}{1} = \sqrt 5 $
