Question

Решите уравнение: сos=1/2 , пожалуйста подробно.

Answer 1

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Answer 2

Solving the Equation cos(x) = 1/2

To solve the equation cos(x) = 1/2, we can use the inverse cosine function to find the values of x for which the cosine of x is equal to 1/2.

The inverse cosine function, also known as arccosine, is denoted as arccos or cos^-1. It gives the angle whose cosine is a given number.

Using the inverse cosine function, we can express the solution as: x = arccos(1/2) + 2πn and x = -arccos(1/2) + 2πn, where n is an integer.

The value of arccos(1/2) is π/3.

Therefore, the solutions for the equation cos(x) = 1/2 are: x = π/3 + 2πn and x = -π/3 + 2πn, where n is an integer.

This means that the solutions for x are all the angles that have a cosine of 1/2, and they occur at intervals of 2π.

Conclusion

The solutions to the equation cos(x) = 1/2 are x = π/3 + 2πn and x = -π/3 + 2πn, where n is an integer. These solutions represent the angles at which the cosine function equals 1/2.