3cos^2x-sin^2x+4sinx=0,
3(1-sin^2x)-sin^2x+4sinx=0,
3-4sin^2x+4sinx=0,
4sin^2x-4sinx-3=0,
sinx=t,
4t^2-4t-3=0,
D=64,
t1=-1/2,
t2=1.5>1
sinx=-1/2,
x=(-1)^k arcsin(-1/2)+pi*k, kєZ,
x=(-1)^(k+1) arcsin(1/2)+pi*k, kєZ,
x=(-1)^(k+1) pi/6+pi*k, kєZ
3cos^2x-sin^2x+4sinx=0
4sinx^2-4sinx-3=0
4x2 - 4x - 3 = 0D = b2 - 4acD = 16 + 48 = 64 = 8^2
x1,2 = -b ± √D/2ax1 = 4 + 8/8 = 12/8 = 3/2x2 = 4 - 8/8 = - 4/8 = - 1/2ответ: x2 = - 1/2
sin(x2)=-0,5
3cos^2x-sin^2x+4sinx=0,
3(1-sin^2x)-sin^2x+4sinx=0,
3-4sin^2x+4sinx=0,
4sin^2x-4sinx-3=0,
sinx=t,
4t^2-4t-3=0,
D=64,
t1=-1/2,
t2=1.5>1
sinx=-1/2,
x=(-1)^k arcsin(-1/2)+pi*k, kєZ,
x=(-1)^(k+1) arcsin(1/2)+pi*k, kєZ,
x=(-1)^(k+1) pi/6+pi*k, kєZ
3cos^2x-sin^2x+4sinx=0
4sinx^2-4sinx-3=0
4x2 - 4x - 3 = 0
D = b2 - 4ac
D = 16 + 48 = 64 = 8^2
x1,2 = -b ± √D/2a
x1 = 4 + 8/8 = 12/8 = 3/2
x2 = 4 - 8/8 = - 4/8 = - 1/2
ответ: x2 = - 1/2
sin(x2)=-0,5