Макс. решить!

1. Решите уравнения:

1) cos (x/3) = -1

2) ctg ((2x)/7) = 1

3) tg(7x + π/6) = 4,1

4) 2cos ((x/11) - (π/6)) + √3 = 0

5) -2sin(4x - π/9) = -0,4

6) 3cos x - 2 sin x = 0

7) 4cos▲2 (x/5) -3 = 0

8) 3sin x - 2 cos x = 3

9) sin(5π/√x) = -(1/2)

10)5sin▲2 (2x) - 21 cos 2x - 9 = 0

11) sin(4x) + sin(5x) = 0

12) - (1/√3) sin (x) cos (x) + sin ▲2 (x) = 1/2

13) 2 cos▲2 (2x) + cos (10x) - 1 = 0

14) Найдите наибольший отрицательный корень уравнения:

tg(π/6 - 4x) ctg(3x - π/9) = 0

1. cos (x/3) = -1

x/3 = π + 2πk, k∈Z

2. ctg ((2x)/7) = 1

ctg ((2x)/7) = 1,  x≠((7πk)/2),  k∈Z

(2x)/7 = arcctg(1)

(2x)/7 = π/4 + πk,  k∈Z

8x = 7π + 28πk, k∈Z

x = (7π)/8 + (7πk)/2,  k∈Z

3) tg(7x + π/6) = 4,1

tg(7x + π/6) = 4,1,  x≠π/21 + πk/7, k∈Z

7x = arctg(4,1) -  π/6 +πk,  k∈Z

x = (arctg(4,1))/7 - π/42 + πk/7, k∈Z

4) 2cos ((x/11) - (π/6)) + √3 = 0

2cos ((x/11) - (π/6)) = -√3

cos ((x/11) - (π/6))= -(√3/2)

ответ: x=11π + 22πk, k∈Z; x=(44π)/3 + 22πk, k∈Z

5) -2sin(4x - π/9) = -0,4

4x - π/9 = arcsin(1/5)

sin(10π/9 - 4x)=1/5

ответ: x= (arcsin(1/5))/4 + π/36 + πk/2, k∈Z; (arcsin(1/5))/4 + 5π/18 + πk/2, k∈Z

6) 3cos x - 2 sin x = 0

2sin x = 3cos x    | /cos x

2tg x = 3

tg x = 3/2

x = arctg(3/2) + πk, k∈Z

7) 4cos²(x/5) -3 = 0

4cos²(x/5) = 3

cos²(x/5) = 3/4

cos(x/5) = ±((√3)/2)

ответ: x = 5π/6 + 5πk, k∈Z; x = 25π/6 + 5πk, k∈Z

8) 3sin x - 2 cos x = 3

3 * (2t/(1+t²)) - 2((1-t²)/(1+t²)) = 3

t=1

t=5

tg(x/2) = 1

tg(x/2) = 5

x = π/2 + kπ, k∈Z; x=2arctg5 + 2kπ, k∈Z

Пошаговое объяснение: