Question

URGENTE- Considerando $\frac{3\pi}{2} < x < 2\pi$ e dado o valor de cos x = $\frac{2}{3}$ , determine:

a) sen x =
b) tg x =
c) cotg x =
d) sec x =
e) cossec x =

Answer 1

Olá!

Utilizando das identidades trigonométricas:

a) Sen^2 x + 4 / 9 = 1

Sen^2 x = 5 / 9

Sen x = √5 / 3

b) tg x = √5 / 3 / 2 / 3 --> √5 / 3 . 3 / 2 -->

3√5 / 6 --> √5 / 2

c) cotg x = 2 / √5 --> 2√5 / 5

d) tg ^2 x + 1 = sec ^2 x

5 / 4 + 1 = sec ^2 x

sec x = 3 / 2

e) 1 + cotg^2 x = cossec ^2 x

1 + 20 / 25 = cossec ^2 x

cossec^2 x = 45 / 25

cossec x = 3√5 / 5


Qualquer dúvida me fala.