Question

fie x,y apartine (pi, 3pi/2) astfel incat sinx=-1/3
siny=-2/3
calculati cos(x-y)​

Answer 1

Răspuns:

Explicație pas cu pas:

cos(x-y) = cosx*cosy +sinx*siny

cos^2(x) = 1 -sin^2(x) = 1- 1/9 = 8/9

cosx = -+ √8/9 = -+2√2/3 , x in  (pi, 3pi/2) ,

deci cosx = -2√2/3

cos^2(y) = 1 -sin^2(y) = 1 -4/9 = 5/9

cosy = -+√5/9 = -+√5/3 , y in  (pi, 3pi/2) ,

deci cosy = -√5/3

cos(x-y) = -2√2/3*(-√5/3) + (-1/3*(-2/3)) =

2√10/9 + 2/9 = 2/9(√10 +1)