Question

Wyznacz wartości funkcji trygonometrycznych kątów ostrych trójkąta prostokątnego o bokach: 9 12 15

Answer 1

a = 9

b = 12

c = 15

sin α = a/c = 9/15 = 3/5

cos α = b/c = 12/15 = 4/5

tg α = a/b = 9/12 = 3/4

ctg α = b/a = 4/3

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sin β = b/c = 12/15 = 4/5

cos β = a/c = 9/15 = 3/5

tg β = b/a = 12/9 = 4/3

ctg β = a/b =9/12 = 3/4

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Answer 2

dane:

AB =a = 9

BC =b = 12

AC =c = 15

Kąt prosty między ramionami AB i BC

szuk.:

sin(a)

cos(a)

tg(a)

ctg(a)

sin(b)

cos(b)

tg(b)

ctg(b)

Kąt alfa(przy A), kąt beta(przy C))

 

sin(a) =b/c =12/15 = 4/5 = 0,8

cos(a) = a/c =9/15 = 3/5 = 0,6

tg(a) = b/a =12/9 = 4/3 =1,(33)

ctg(a) =a/b = 9/12 =3/4 = 0,75

 

sin(b) = a/c =9/15 =3/5 = 0,6

cos(b) = b/c =12/15 = 4/5 =0,8

tg(b) = a/b = 9/12 =3/4 = 0,75

ctg(b) =b/a =12/9 = 4/3 =1,(33)