Question

Dado o sen x 1/4, com 0< x < π/2, calcule o cos x.

Answer 1

$\sqrt[2]{15} / 4$

Aplicando-se a equação fundamental da trigonometria tem-se:

$sen^2x + cos^2x = 1\\\\(1/4)^2 + cos^2x = 1\\\\1/16 + cos^2x= 1\\\\cos^2x = 1 - 1/16\\\\cos^2x = (16 - 1) / 16\\\\cos^2x = 15 / 16\\\\cosx = \sqrt[2]{\frac{15}{16} }\\\\cox = \sqrt[2]{15} / 4$

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