Question

Решите неравенство cost>1/2 очень срочно

Answer 1

Ответ:

$cost > \frac{1}{2};\\\\-arccos\frac{1}{2}+2\pi n < t < arccos\frac{1}{2}+2\pi n, n \in Z;\\\\-\frac{\pi}{3}+2\pi n < t < \frac{\pi}{3}+2\pi n, n \in Z;\\\\t \in (-\frac{\pi}{3}+2\pi n, \frac{\pi}{3}+2\pi n), n \in Z;$

Answer 2

Solving the Inequality cos(x) > 1/2

To solve the inequality cos(x) > 1/2, we need to find the values of x for which the cosine function is greater than 1/2.

The cosine function represents the ratio of the adjacent side to the hypotenuse in a right-angled triangle for a given angle. When the cosine of an angle is greater than 1/2, it means that the adjacent side is longer than half the length of the hypotenuse.

Solution Steps

1. Identify the Range of x: The cosine function has a period of 2π, so we can consider the values of x within one period (0 to 2π). 2. Find the Critical Points: We need to find the critical points where cos(x) = 1/2. 3. Determine the Solution Set: Based on the critical points, we can determine the intervals where cos(x) > 1/2.

Critical Points

The critical points occur when cos(x) = 1/2. The solutions lie in the first and fourth quadrants, where the cosine function is positive.

Solution

The solutions to the inequality cos(x) > 1/2 are within the intervals where the cosine function is greater than 1/2.

Conclusion

The solutions to the inequality cos(x) > 1/2 are within specific intervals in the first and fourth quadrants.