Cos x = - 1/√2 решить уравнение

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вопрос

To solve the equation cos(x) = -1/√2, we need to determine the values of x that satisfy this equation.

Since the cosine function is negative in the second and third quadrants, we can find the reference angle whose cosine is 1/√2 and then find the corresponding angles in those quadrants.

The reference angle whose cosine is 1/√2 is π/4 (45 degrees).

In the second quadrant, the angle whose cosine is -1/√2 is π - π/4 = 3π/4 (135 degrees).

In the third quadrant, the angle whose cosine is -1/√2 is 2π - π/4 = 7π/4 (315 degrees).

Therefore, the solutions to the equation cos(x) = -1/√2 are:

x = 3π/4 + 2πn, where n is an integer
x = 7π/4 + 2πn, where n is an integer.