Mathematics: Given sin A = 4/5 and cos A 0, find tan A

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Given sin A = 4/5 and cos A 0, find tan A - id4506225518, orlandocruz42

marcosrodriguez5304

25.01.2022

tan A = - $\frac{4}{3}$

Step-by-step explanation:

Using the identity sin² A + cos² A = 1, then

( $\frac{4}{5}$ )² + cos² A = 1

$\frac{16}{25}$ + cos² A = 1 ( subtract $\frac{16}{25}$ from both sides )

cos² A = $\frac{9}{25}$ ( take the square root of both sides )

cos A = ± $\sqrt{\frac{9}{25} }$ and given cosA < 0, then

cos A = - $\frac{3}{5}$

Using the identity

tan A = $\frac{sinA}{cosA}$ , then

tan A = $\frac{\frac{4}{5} }{-\frac{3}{5} }$ = $\frac{4}{5}$ × - $\frac{5}{3}$ = - $\frac{4}{3}$

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