Question

Sabendo que x € 1° quadrante e que sec x = 5/3, calcule tg x

Answer 1

$sec^2x = tg^2x + 1\\ \\ tg^2 = sec^2x - 1\\ \\ tg^2x = (\frac{5}{3})^2 - 1 \\ \\ tg^2x = \frac{25}{9}-1 \\ \\ tg^2x = \frac{25-9}{9} \\ \\ tg^2x = \frac{16}{9} \\ \\ tgx = \sqrt{ \frac{16}{9} } \\ \\ tgx = \frac{4}{3}$
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Portanto, a tgx = 4/3