Dau coroana si dau 50 de puncte
Rezolvati va rog tabelele acelea :( ca imi trebuie neaparat
Răspunsuri la întrebare
sin x = cateta opusa / ipotenuza
cos x = cateta alaturata / ipotenuza
tg x = cateta opusa / cateta alaturata
ctg x = cateta alaturata / cateta opusa
Pitagora
ip² = c₁² + c₂²
AB, AC = catete
BC = ipotenuza
1)
a) AB = 12, AC = 16
BC = √AB² + AC² = √144 + 256 = √400 = 20 cm
sinB = AC/BC = 16/20 = 4/5
cosB = AB/BC = 12/20 = 3/5
sinC = AB/BC = 12/20 = 3/5
cosC = AC/BC = 16/20 = 4/5
tgB = AC/AB = 16/12 = 4/3
tgC = AB/AC = 12/16 = 3/4
ctgB = AB/AC = 12/16 = 3/4
ctgC = AC/AB = 16/12 = 4/3
b)
AC = √900 - 324 = √576 = 24 cm
sinB = 24/30 = 4/5
sinC = 18/30 = 3/5
cosB = 18/30 = 3/5
cosC = 24/30 = 3/5
tgB = 24/18 = 4/3
tgC = 18/24 = 3/4
ctgB = 18/24 = 3/4
ctgC = 24/118 = 4/3
c)
AB = √1225 - 441 = √784 = 28 cm
sinB = 21/35 = 3/5
sinC = 28/35 = 4/5
cosB = 28/35 = 4/5
cosC = 21/35 = 3/5
tgB = 21/28 = 3/4
tgC = 28/21 = 4/3
ctgB = 28/21 = 4/3
ctgC = 21/28 = 3/4
Punctele d), e) si f) le faci singur sa exersezi.
2)
a)
BC = √2304 - 11296 = √1008 = √2⁴·3²·7 = 12√7 cm
sinB = AC/BC = 48/12√7 = 4/√7 = 4√7/7
sinC = AB/BC = 36/12√7 = 3/√7 = 3√7/7
cosB = AB/BC = 36/12√7 = 3/√7 = 3√7/7
cosC = AC/BC = 48/12√7 = 4/√7 = 4√7/7
tgB = AC/AB = 48/36 = 4/3
tgC = AB/AC = 36/48 = 3/4
ctgB = AB/AC = 36/48 = 3/4
ctgC = AC/AB = 48/36 = 4/3
b)
AC = √90² - 54² = √8100 - 2916 = √5184 = 72 cm
sinB = 72/90 = 4/5
sinC = 54/90 = 3/4
cosB = 54/90 = 3/4
cosC = 72/90 = 4/5
tgB = 72/54 = 4/3
tgC = 54/72 = 3/4
ctgB = 54/72 = 3/4
ctgC = 72/54 = 4/3
AB = √105² - 84² = √11025 - 7056 = √3969 = 63 cm
sinB = 84/105 = 4/5
sinC = 63/105 = 3/5
cosB = 63/105 = 3/5
cosC = 84/105 = 4/5
tgB = 84/63 = 4/3
tgC = 63/84 = 3/4
ctgB = 63/84 = 3/4
ctgC = 84/63 = 4/3
d)
AB = √6√30² - 12√2² = √1080 - 288 = √792 = √2³·3²·11 = 6√22 cm
sinB = 12√2/6√30 = √30/15
sinC = 6√11/6√30 = √330/30
cosB = 6√11/6√30 = √330/30
cosC = 12√2/6√30 = √30/15
tgB = 12√2/6√11 = 2√22/11
tgC = 6√11/12√2 = √22/4
ctgB = 6√11/12√2 = √22/4
ctgC = 12√2/6√11 = 2√22/11
