Question

Sendo senx = 4/5 e cosy = 12/13, com x e y o 1º quadrante, determine o valor de sen (x + y) :
A. 45/63
B. 65/63
C. 63/65
D. 63/45
E. 1

Answer 1

Resposta:

a:hipotenusa

b:cateto oposto

c:cateto adjacente

ângulos do 1ª Quadrante  ==> sen, cos e tan > 0

sen(x) = 4/5 =b/a ==> b=4a/5

a²=b²+c²

a²=(4a/5)²+c²

a²=16a²/25+c²

25a²=16a²+25c²

a²=25c²/9 ==>a=5c/3

cos(x)=c/a=c/(5c/3) =3/5

cos(y)=12/13=c/a ==> c=12a/13

a²=b²+c²

a²=b²+(12a/13)²

a²=b²+144a²/169

169a²=144a²+169b²

25a²=169b²

a=13b/5

sen(y)=b/a=b/(13b/5)=5/13

sen(x+y)=sen(x)*cos(y) +sen(y)*cos(x)

sen(x+y)=(4/5) *(12/13)+ (5/13)*(3/5)

sen(x+y)=48/65+ 15/65 =63/65

Letra C