Question

Решить неравенство cosx>=0,9

Answer 1

Решение задания смотри на фотографии

Answer 2

To solve the inequality cos(x) >= 0.9, we need to find the range of x that satisfies the given condition. Let's proceed step by step:

1. First, find the solutions for cos(x) = 0.9: To do this, we can take the inverse cosine (arccos) of both sides of the equation: x = arccos(0.9)

2. Calculate the value of arccos(0.9): Using a calculator, we find that arccos(0.9) ≈ 25.84 degrees or 0.451 radians.

3. Determine the principal solution in the interval [0, 2π]: The cosine function is positive in the first and fourth quadrants. Since cos(x) = 0.9 is positive, we only need to consider the first quadrant. So, the principal solution lies between 0 and π/2 (0 and 90 degrees).

4. Find the general solution for the inequality: The general solution is given by: x ≥ arccos(0.9)

5. Convert the angle to degrees (if required): If the question asks for the solution in degrees, convert the radian value of arccos(0.9) to degrees: x ≥ 25.84 degrees

So, the solution to the inequality cos(x) ≥ 0.9 is x ≥ 25.84 degrees (or x ≥ 0.451 radians). This means any value of x greater than or equal to 25.84 degrees (or 0.451 radians) will satisfy the inequality.