Question

Y=4 sinxsin(x-60) mencapai nilai minimum pada...
a. x=60'+k.360', k=0,1,2,...
b. x=60'+k.180', k=0,1,2,...
c. x=30'+k.360', k=0,1,2,...
d. x=30'+k.180', k=0,1,2,...
e.x=k.360', k=0,1,2,...

Answer 1

Y = 4 sin x . sin (x - 60)
y = -2 (-2. sin x - sin (x - x - 60)) -> Jumlah dan selisih dua sudut
y = -2 (cos (x + x - 60) - sin (60))
y = -2 (cos(2x - 60) - 1/2)
y = - 2 cos(2x-60) - 1
Nilai akan minimum jika fungsinya bernilai -1
-1 = -2 cos (2x-60) -1
-2 cos (2x-60) = -2
cos (2x-60) = 1
cos (2x-60) = cos 0
2x - 60 = 0 + k.360
2x = 60 + k.360

x = 30 + k.180
Jawabannya D.