Question

50 PONTOS!!
Sendo cossec(x) = -4 e 3π/2 < x < 2π calcule:
a) sen(x)
b) cos(x)
c) sec(x)
d) tg(x)
e) cotg(x)

Answer 1

a)
$\csc( \alpha ) = \frac{1}{ \sin( \alpha ) }$
$\sin(x) = - \frac{1}{4}$
b)
$\sin ^{2} (x) + \cos ^{2} (x) = 1$
$\cos(x) = \sqrt{1 - \frac{1}{16} }$
c)
$\sec(x) = \frac{1}{ \cos(x) }$
$\sec(x) = \frac{1}{ \sqrt{1 - \frac{1}{16} } }$
d)
$\tan(x) = \frac{ \sin(x) }{ \cos(x) } \\ \tan(x) = - \frac{ 1}{4} \times \frac{1}{ \sqrt{1 - \frac{1}{16} } } \\ \tan(x) = - \frac{1}{4 \times \sqrt{1 - \frac{1}{16} } }$
e)
$\cot(x) = \frac{1}{ \tan(x) } \\ \cot(x) = - 4 \times \sqrt{1 - \frac{1}{16} }$