Answer
Required trigonometric functions are-
$\sin A = \frac{1}{\sqrt 2}$ , $\\csc A = \sqrt 2$
$\\cos A = \frac{1}{\sqrt 2}$ , $\\sec A = \sqrt 2$
$\\tan A = 1$ , $\\\cot A = 1$
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)
$c^{2} =1^{2} + 1^{2}$
$c^{2} = 1 + 1$
$c^{2} = 2$
therefore $ c = \sqrt 2$
Now we can write the required six T-functions of A using a = 1, b=1 and $c = \sqrt 2$
$\sin A = \frac{a}{c} = \frac{1}{\sqrt 2}$
$\\csc A = \frac{c}{a} = \frac{\sqrt 2}{1}$ = $\sqrt 2$
$\\cos A = \frac{b}{c} =\frac{1}{\sqrt 2}$
$\\sec A = \frac{c}{b} = \frac{\sqrt 2}{1}$ = $\sqrt 2$
$\\tan A = \frac{a}{b} = \frac{1}{1}$ = 1
$\\\cot A = \frac{b}{a} = \frac{1}{1}$ = 1
