Триганометрические, составитель ошибся
а)sin x = ✓3/2
x = (-1)ⁿ π/3 + πn
б)cos x = -3/5
x = ±arccos(-3/5) + 2πk
x = ±(π-arccos(3/5)+2πk
в)2cos²x+cosx - 1 = 0
cos x = t
2t²+t-1 = 0
Так как a-b+c = 0(2-1-1 = 0):
t1 = -1
t2 = -c/a = 1/2
1)cos x = -1
x = π+2πn
2)cos x = 1/2
x = ±π/3 + 2πn
г)sinx + sin 3x + sin 5x = 0
sin3x + sin5x + sinx = 0
sin3x + 2sin3x • cos2x = 0
sin3x(1+2cos2x) = 0
1)sin 3x = 0
3x = πk
x = π/3 k
2)1+2cos2x = 0
2cos2x = -1
cos2x = -1/2
2x = ±(π-arccos(1/2) + 2πk
x = ±1/2(π-π/3)+πk
x = ±1/2(2π/3)+πk
x = ±π/3 + πk
Триганометрические, составитель ошибся
а)sin x = ✓3/2
x = (-1)ⁿ π/3 + πn
б)cos x = -3/5
x = ±arccos(-3/5) + 2πk
x = ±(π-arccos(3/5)+2πk
в)2cos²x+cosx - 1 = 0
cos x = t
2t²+t-1 = 0
Так как a-b+c = 0(2-1-1 = 0):
t1 = -1
t2 = -c/a = 1/2
1)cos x = -1
x = π+2πn
2)cos x = 1/2
x = ±π/3 + 2πn
г)sinx + sin 3x + sin 5x = 0
sin3x + sin5x + sinx = 0
sin3x + 2sin3x • cos2x = 0
sin3x(1+2cos2x) = 0
1)sin 3x = 0
3x = πk
x = π/3 k
2)1+2cos2x = 0
2cos2x = -1
cos2x = -1/2
2x = ±(π-arccos(1/2) + 2πk
x = ±1/2(π-π/3)+πk
x = ±1/2(2π/3)+πk
x = ±π/3 + πk