Question

If tan A= 5/12 , find the other trigonometric ratios of the angle A.

Answer 1

Step-by-step explanation:

$tan \: A \: = \frac{5}{12} = \frac{perpendicular}{base} \\ {hyp}^{2} = \: {perp}^{2} + {base}^{2} \\ = {5}^{2} + {12}^{2} = 25 + 144 = 169 \\ hyp = 13 \\ now \\ sin \: A \: = \frac{perp}{hyp} = \frac{5}{13} \\ cos \: A \: = \frac{base}{hyp} = \frac{12}{13} \\ tan \: A \: = \frac{perp}{base} = \frac{5}{12} \\ \\ cot \: A \: = \frac{base}{perp} = \frac{12}{5} \\ sec \: A \: = \frac{hyp}{base} = \frac{13}{12} \\ cosec \: A \: = \frac{hyp}{perp} = \frac{13}{5}$

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