Question

sen x = 3/8
calcule
cos x=
tag x=
sec x =
cossec x

Answer 1

sen²x + cos²x = 1   --> Identidade Trigonometrica

(3/8)² + cos²x = 1

cos²x = 1 - 9/64

cos²x = 55/64

$cos\,x=\sqrt{\frac{55}{64}} \;=\;\frac{\sqrt{55}}{8}$

tg x = senx / cosx

$tg\,x=\frac{\frac{3}{8}}{\frac{\sqrt{55}}{8}}\\\\tg\,x=\;\frac{3}{\sqrt{55}}\\\\tg\,x=\frac{3}{\sqrt{55}}.\frac{\sqrt{55}}{\sqrt{55}}\\\\tg\,x=\frac{3\sqrt{55}}{55}$

sec x = 1 / cos x

$sec\,x=\frac{1}{\frac{\sqrt{55}}{8}}\\\\sec\,x=\frac{8}{\sqrt{55}}\\\\sec\,x=\frac{8}{\sqrt{55}}.\frac{\sqrt{55}}{\sqrt{55}}\\\\sec\,x=\frac{8\sqrt{55}}{55}$

cossec x = 1 / sen x

cossec x = 1 / (3/8)

cossec x = 8/3