Question

Cosx<-1/√3 решите тригонометрические уравнения

Answer 1

Решение задания смотри на фотографии

Answer 2

To solve the trigonometric equation cos(x) < -1/√3, we need to find the values of x that satisfy the inequality. Let's proceed with the solution:

1. Find the critical points where cos(x) = -1/√3: To find critical points, we look for solutions to the equation cos(x) = -1/√3.

cos(x) = -1/√3

To find the solutions, we take the arccosine of both sides:

x = arccos(-1/√3)

Using a calculator, we find that arccos(-1/√3) ≈ 150.00°.

Now, since cos(x) is a periodic function, the solutions repeat at intervals of 360°. So, we can find more solutions by adding or subtracting multiples of 360° to the critical point:

Additional solutions: x = 150.00° ± 360°, or in radians x = 150.00° ± 2π.

2. Find the solution in the desired range (-180° to 180° or -π to π): The solutions that lie in the range from -180° to 180° are:

x ≈ -150.00°, or in radians, x ≈ -2.62. x ≈ 210.00°, or in radians, x ≈ 3.67.

So, the solutions to the trigonometric inequality cos(x) < -1/√3 in the range from -180° to 180° (or -π to π in radians) are approximately -2.62 and 3.67.