Question

Sabendo que sen(x)=3/5 e pertence ao 1 quadrante, calcule:
a) cos (x)
b) tg (x)
c) cotg (x)
d) sec (x)
e) cossec (x)

Answer 1

a) utilizando a relação fundamental
sen²x + cos²x = 1
(3/5)² + cos²x = 1
cos x = 4/5

b) tgx = senx/cosx = $\frac{ \frac{3}{5} }{ \frac{4}{5} }$
tgx = 3/4

c) cotg = 1/tgx
cotg = $\frac{1}{ \frac{3}{4} }$
cotg x = 4/3

d) secx = 1/cosx
secx = $\frac{1}{ \frac{4}{5} }$
secx = 5/4

e) cossecx = 1/senx
cossecx = $\frac{1}{ \frac{3}{5} }$
cossecx = 5/3

Answer 2

a)    cos(x)

 

       sen(x)=3/5

     cos (x) = ?

 

sen²(x) + cos²(X) = 1

               cos²(X) = 1 - sen²(x)

               cos²(X) = 1 – (3/5) ²

               cos²(X) =  1 – 9 /25

               cos²(X)  =  16/25

               cos (X)   = V 16/25

               cos (X)   =       4 /5

 

Resposta : a) 4/5

                                                                                      

 

b)    tg (x) 

 

sen(x)  = 3/5  =   3/4

         cos(x)     4 /5

 

                                                                                      

 

 

c)    cotg (x) = 1/tg(x)   =  cos(x)

                                      sen (x)

 

                                       4/5 : 3/5   =

                               4/5 X 5/3 =   4/3

 

 

 

 

 

d)    sec (X) 

 

sec(X) = 1/cos(X)  = 1

                                cos(X)

 

sec(X)                    = 1

                                 4/5

 

sec(X)                    =  5/4

 

                                                                                                                         

e)    cossec (x) = 1/ se(X)

                          1/ 3/5   = 5/3

 

              

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