Question

Cosx = π/2 тринометрическое уровнение

Answer 1

Cosx = π/2
x=arccos(пи/2)+2пиN N принадлежит z
x=2пиN N принадлежит z

Answer 2

Trigonometric Equation: cos(x) = π/2

The trigonometric equation you provided is cos(x) = π/2. This equation represents the cosine function of an angle x, which is equal to π/2.

To solve this equation, we need to find the values of x that satisfy the equation.

Solution:

To find the solutions to the equation cos(x) = π/2, we can use the properties of the cosine function and the unit circle.

The cosine function represents the x-coordinate of a point on the unit circle. The value of π/2 corresponds to the point (0, 1) on the unit circle.

Since the cosine function repeats every 2π radians, we can find the solutions by adding or subtracting multiples of 2π to the initial solution.

Therefore, the solutions to the equation cos(x) = π/2 are:

- x = π/2 + 2πn, where n is an integer.

In other words, x can take on any value that is π/2 plus a multiple of 2π.

Example Solution:

Let's find one solution to the equation cos(x) = π/2.

By inspection, we can see that one solution is x = π/2.

To verify this solution, we can substitute x = π/2 into the equation:

cos(π/2) = π/2

Using the unit circle, we can see that cos(π/2) = 0.

Therefore, the solution x = π/2 satisfies the equation.

Additional Information:

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