Question

Determine os valores de tg x ,cotg x,sec x e cossec x sabendo que cos x =2/7 e que angulo x encontra se no 3° quadrante .

Answer 1

sen²x + cos²x = 1
sen²x = 1 - cos²x
sen²x = 1 - (2/7)²
sen²x = 1 - 4/49
sen²x = 49 - 4/49
sen²x = 45/49
sen x = √45/√49
sen x = √45/7

Tg = sen x/cos x
Tg = √45/7/2/7
Tg = √45/2

Cotg x = cos x/sen x
Cotg x = 2/7/√45/7
Cotg x = 2/√45 (Racionalização ) (fator comum √45)

Cotg x = 2√45/45

sec x = 1/cos x
Sec x = 1/2/7
sec x = 7/2

cossec x = 1/sen x
cossec x = 1/√45/7
cossec x = 7/√45
cossec x = 7√45/45