Question

Me ajudem!
Dado sen x=4/3 e pi/2 < x < pi, calcule:
a) cos x
b) tg x
c) sex x
d) cossec x
e) cotg x

Answer 1

 sen x = 4/3   o sen x deve ser 3/4 

sen² x + cos² x = 1
(3/4)² + cos ² x = 1
9/16 + cos ² x = 1
cos² x = 1 - 9/16
cos² x = 16/16 - 9/16
cos² x = 7/16
cos x = √7/16
cos x = - √7/4
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tg x = sen x/cos x
tg x =   3/4 : ( - √7/4)
tg x = 3/4 . ( - 4/√7)
tg x = - 12/4√7              Racionalizando
tg x = - 12.√7/4.√49
tg x = - 12√7/28            simplifique por 4
tgx = - 3√7/7
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cotg x = cos x/sen x
cotg x = - √7/4 : 3/4
cotg x = - √7/4 . 4/3
cotg x = - 4√7/12          simplifique por 4
cotg x = - √7/3
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sec x = 1/cosx
sec x = 1 : ( - √7/4)
sec x = 1 . ( - 4√7)
sec x = - 4/√7               Racionalizando
sec x = - 4√7 . √7/√7
sec x = - 4√7/√49
sec x = - 4√7/7
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cossec x = 1/senx
cossec x = 1 : 4/3
cossec x = 1 . 3/4
cossec x = 3/4