Question

Cos X =-1/2???????????????????????????

Answer 1

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                                                                                                                   cos x=-1/2 х=+(п-arccos-1/2)+2пn х=+ п -п/3+2пnх= +  2п/3+2пn,где n-цел.числа                              

Answer 2

To find the value of x that satisfies the equation cos(x) = -1/2, we can use the inverse cosine function (also known as arccosine or cos^(-1)).

The inverse cosine function "undoes" the cosine function and gives us the angle whose cosine is a given value. In this case, we want to find the angle x such that cos(x) = -1/2.

Using the inverse cosine function, we can write:

x = arccos(-1/2)

To find the value of x, we can use a calculator or a trigonometric table. The principal value of arccos(-1/2) is 120 degrees (or 2π/3 radians). However, cosine is a periodic function, and it repeats every 360 degrees (or 2π radians). So, there are other values of x that satisfy the equation.

The general solution can be written as:

x = 2nπ ± arccos(-1/2)

where n is an integer.

In degrees, the solutions are:

x ≈ 120° + 360°n and x ≈ 240° + 360°n

In radians, the solutions are:

x ≈ 2π/3 + 2πn and x ≈ 4π/3 + 2πn

Please note that there are infinitely many solutions since the cosine function has a periodic nature.