Question

oblicz SIN, COS ,TG i CTG dla a) tg=4/3 b)ctg=45/28

Answer 1

a)

tg=4/3

ctg=3/4

tg=4/3=sin/cos=sin/(pierw(1-sin^2))  

    4/3=sin/(pierw(1-sin^2))   /*(pierw(1-sin^2)        

    4/3 *PIERW(1-SIN^2) =sin  /*3

 4*pierw(1-sin^2)=3sin     /^2

 16(1-sin^2)=9sin^2

16-16sin^2=9sin^2

16=9sin^2+16sin^2

16=25sin^2   /:25

16/25=sin^2

sin=4/5

 

cos=pierw(1-sin^2)=pierw(1-16/25)=pierw(9/25)=3/5

cos=3/5

b)

ctg=45/28

tg=28/45

tg=28/45=sin/cos=sin/(pierw(1-sin^2))  

    28/45=sin/(pierw(1-sin^2))   /*(pierw(1-sin^2)        

    28/45 *PIERW(1-SIN^2) =sin  /*45

 28*pierw(1-sin^2)=45sin     /^2

 784(1-sin^2)=2025sin^2

784-784sin^2=2025sin^2

784=2025sin^2+784sin^2

784=2809sin^2

sin^2=784/2809

sin=28/53

cos=pierw(1-sin^2)=pierw(1-784/2809)=pierw(2025/2809)=45/53

cos=45/53