Answer
Required six T-functions are-
$\sin A = \frac{3}{4}$ , $\\csc A = \frac{4}{3}$
$\\cos A = \frac{\sqrt 7}{4}$ , $\\sec A = \frac{4}{\sqrt 7}$
$\\tan A = \frac{3}{\sqrt 7}$ , $\\\cot A = \frac{\sqrt 7}{3}$
Work Step by Step
Steps to Answer-
First we will draw the diagram of triangle ABC and then use the given information and Pythagoras Theorem to solve for 'c'-
$c^{2} =a^{2} + b^{2}$
$c^{2} = 3^{2} + (\sqrt 7)^{2}$
$c^{2} = 9 + 7$
$c^{2} = 16$
therefore $ c = \sqrt 16$ = 4
Now we can write the required six T-functions of A using a = 3, $b= \sqrt 7$ and c = 4
$\sin A = \frac{a}{c} = \frac{3}{4}$
$\\csc A = \frac{c}{a} = \frac{4}{3}$
$\\cos A = \frac{b}{c} = \frac{\sqrt 7}{4}$
$\\sec A = \frac{c}{b} = \frac{4}{\sqrt 7}$
$\\tan A = \frac{a}{b} = \frac{3}{\sqrt 7}$
$\\\cot A = \frac{b}{a} = \frac{\sqrt 7}{3}$
