Answer
$\sin A = \frac{4}{5}$
$\\cos A = \frac{3}{5}$
$\\tan A = \frac{4}{3}$
$\\csc A = \frac{5}{4}$
$\\\sec A = \frac{5}{3}$
$\\\cot A = \frac{3}{4}$
Work Step by Step
We will use given data about triangle ABC & Pythagoras Theorem to solve for 'a'-
We know that -
$c^{2} =a^{2} + b^{2}$ ( Pythagoras Theorem)
Therefore -
$a^{2} =c^{2} - b^{2}$
$a^{2} = (5)^{2} - (3)^{2}$
$a^{2} = 25 - 9$
$a^{2} = 16$
therefore $ a = \sqrt (16)$
a = 4
Now we can write the required T-functions of A and B using $a=4$ , b = 3 and c = 5
$\sin A = \frac{a}{c} = \frac{4}{5}$
$\\cos A = \frac{b}{c} = \frac{3}{5}$
$\\tan A = \frac{a}{b} = \frac{4}{3}$
$\\csc A = \frac{c}{a} = \frac{5}{4}$
$\\\sec A = \frac{c}{b} = \frac{5}{3}$
$\\\cot A = \frac{b}{a} = \frac{3}{4}$
