Question

ex:5,6 dau 10 puncte

Answer 1

a) cos(x-y) =      x,y apartin(0, pi/2)  Deci sin(x) si sin(y) >0 
cos(x) = 1/7 
sin^2(x) + cos^2(x) =1
sin^2(x) = 1-cos^2(x) = 1- 1/49 = 48/49
sin(x) = v(48/49) =  v48/v49 = 4v3/7
cos(y) = 13/14
sin^2(y) + cos^2(y) =1
sin^2(y) = 1-cos^2(y) = 1- (169/196) = (196-169)/196 = 27/196
sin(y) = v(27/196)= v27/v196 = 3v3/14
cos(x-y) = cos(x)cos(y) +sin(x)sin(y)
cos(x-y) = (1/7)(13/14) + (4v3/7)(3v3/14) = 13/98 + 36/98 = 49/98= 1/2

b) cos(pi/3 -a) =     a apartine (3pi/2 , 2pi) (cadranul IV) cu cos(a) >0
cos(pi/3 -a) = cos(pi/3)cos(a) + sin(pi/3)sin(a)
sin^2(a) +cos^2(a) =1
cos^2(a) = 1 - sin^2(a) = 1 - (-12/13)^2 = 1- (144/169) = (169-144)/169 =25/169
cos(a) = v(25/169) = 5/13
sin(pi/3) = (v3)/2
cos(pi/3) = 1/2
cos(pi/3 -a) = (1/2)(5/13) + [(v3)/2](-12/13) = 5/26 - (12v3)/26