Question

Cos (-x/4)= - корень 2/2

Answer 1

$cos(-\frac{x}4)=-\frac{\sqrt2}2\\ -\frac{x}4=бarccos (-\frac{\sqrt2}{2})+2\pi n, \ \ neZ\\ -\frac{x}4=б(-\frac{\pi}4)+2\pi n, \ \ neZ\\ x=б\pi+8\pi n, \ \ neZ$

Answer 2

To solve the equation cos(-x/4) = -√2/2, we can use the properties of the cosine function. The equation states that the cosine of an angle (-x/4) is equal to -√2/2.

Since the cosine function is an even function, cos(-θ) = cos(θ), we can rewrite the equation as cos(x/4) = -√2/2.

To find the values of x that satisfy this equation, we need to determine when the cosine function equals -√2/2. We can do this by considering the unit circle and identifying the angles where the cosine value is -√2/2.

On the unit circle, the cosine of π/4 radians (45 degrees) is √2/2. Since the cosine function is an even function, the cosine of -π/4 radians (-45 degrees) is also √2/2.

Therefore, we can write the equation as x/4 = π/4 + 2nπ or x/4 = -π/4 + 2nπ, where n is an integer representing the number of complete revolutions around the unit circle.

To find the values of x, we multiply both sides of the equation by 4 to isolate x: For the first case, x = π + 8nπ. For the second case, x = -π + 8nπ.

So, the solutions to the equation cos(-x/4) = -√2/2 are: x = π + 8nπ, x = -π + 8nπ,

where n is an integer.