Question

Me ajuda matheus
Sabendo-se que tgx = -√3/3 e π/2 < x < π, calcule

a) sen x
b) cos x
c) cotg x
d) cossec x
e) sec x

(π se refere ao PI)

Answer 1

tgx = -√3/3 

senx/cos x =-√3/3 

sen x=-cos x * √3/3 

sen²x+cos²x=1

[-cos x * √3/3 ]²+cos²x=1

cos²x *3/9+cos²x=1

(1/3)*cos²x+cos²x=1

cos²x *(1+1/3)=1

cos²x *(4/3)=1
cos²x=3/4
b) cosx=-√3/2    ... π/2 < x < π ...2º Quadrante

a) sen x=-(-√3/2) * √3/3  =3/6=1/2

c) cotg x =1/tang x  =1/(-√3/3)=-3/√3 =-3√3/3=-√3

d) cossec x =1/sen x =1/(1/2)=2

e) sec x =1/cos x =1/[-√3/2]=-2/√3