Answer
Required trigonometric functions are-
$\sin A = \frac{2}{\sqrt 5}$
$\\csc A = \frac{\sqrt 5}{2}$
$\\cos A =\frac{1}{\sqrt 5}$
$\\sec A = \sqrt 5$
$\\tan A = 2$
$\\\cot A= \frac{1}{2}$
Work Step by Step
Steps to Answer-
With the help of given diagram of triangle ABC, we will use the given information and Pythagoras Theorem to solve for 'c'-
$c^{2} =a^{2} + b^{2}$ ( Pythagoras Theorem)
$c^{2} = 1^{2} + 2^{2}$
$c^{2} =1+ 4$
$c^{2} = 5$
therefore $ c = \sqrt 5$
Now we can write the required six T-functions of A using a = 2, b = 1 and $c= \sqrt5$
$\sin A = \frac{a}{c} = \frac{2}{\sqrt 5}$
$\\csc A = \frac{c}{a} = \frac{\sqrt 5}{2}$
$\\cos A = \frac{b}{c} =\frac{1}{\sqrt 5}$
$\\sec A = \frac{c}{b} = \frac{\sqrt 5}{1}$ = $ \sqrt 5$
$\\tan A = \frac{a}{b} = \frac{2}{1}$ = 2
$\\\cot A = \frac{b}{a} = \frac{1}{2}$
