Question

dado cos x = 4/5 e x E 4° quadrate, determine:

a) Sen x
b) Tg x
c) Cotg x
d) Sec x
e) Cossec x

Answer 1

a)

$\sin(x) = - \sqrt{1 - { \cos}^{2}x} \\ \sin(x) = - \sqrt{1 - {( \frac{4}{5} )}^{2} }$

$\sin(x) \\ = - \sqrt{1 - \frac{16}{25} } = - \sqrt{ \frac{9}{25} } = - \frac{3}{5} .$

b)

$\tan(x) = \frac{ \sin(x) }{ \cos(x) } = - \frac{ \frac{3}{5} }{ \frac{4}{5} } = - \frac{3}{4}$

c)

$\cot(x) = \frac{1}{ \tan(x) } = - \frac{4}{3}$

d)

$\sec(x) = \frac{1}{ \cos(x) } = \frac{5}{4}$

e)

$\csc(x) = \frac{1}{ \sin(x) } = - \frac{5}{3}$