Answer
Required trigonometric functions are-
$\sin A = \frac{3}{5}$
$\\csc A = \frac{5}{3}$
$\\cos A = \frac{4}{5}$
$\\sec A = \frac{5}{4}$
$\\tan A = \frac{3}{4}$
$\\\cot A = \frac{4}{3}$
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 'b'-
We know that -
$c^{2} =a^{2} + b^{2}$ ( Pythagoras Theorem)
Therefore -
$b^{2} =c^{2} - a^{2}$
$b^{2} = 10^{2} - 6^{2}$
$b^{2} = 100- 36$
$b^{2} = 64$
therefore $b = \sqrt 64$ = 8
Now we can write the required six T-functions of A using a = 6 , b = 8 and c = 10
$\sin A = \frac{a}{c} = \frac{6}{10} = \frac{3}{5}$
$\\csc A = \frac{c}{a} =\frac{10}{6} = \frac{5}{3}$
$\\cos A = \frac{b}{c} = \frac{8}{10} = \frac{4}{5}$
$\\sec A = \frac{c}{b} = \frac{10}{8} = \frac{5}{4}$
$\\tan A = \frac{a}{b} =\frac{6}{8} = \frac{3}{4}$
$\\\cot A = \frac{b}{a} = \frac{8}{6} = \frac{4}{3}$
