Question

Sendo tg(x) = 5/12 e pi < x < 3pi/2, encontre:

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

Answer 1

tg(x)=5/12 
          
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pi<x<3pi/2  ...3ª quadrante ==>sen  e cos x<0

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sen(x)/cos(x)=5/12

sen(x)=(5/12)*cos(x)

sen²(x)+cos²(x)=1

[(5/12)*cos(x)]² +cos²(x)=1

(25/144)*cos²(x)+cos²(x)=1

cos²(x) * (25/144+1)=1

cos²(x) * (169/144) =1

cos²(x) = 144/169

cos(x)=12/13  ou cos(x)=-12/13

Como é do 3ª quadrante cos(x)=-12/13

sen(x)=(5/12)*cos(x)

sen(x)=(5/12) * (-12/13) =-5/13

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a)cos(x)=-12/13

b)sen(x)=-5/13

c)cogt(x)=cos(x)/sen(x) =(-12/13)/(-5/13) =12/5

d)sec(x)=1/cos(x) =-13/12

e)cossec(x)=1/sen(x)=1/(-5/13)=-13/5