Question

Cos 3x = – 1/корень из 2

Answer 1

Ответ:

±π/4 + 2/3 πn, где n∈Z

Пошаговое объяснение:        

cos 3x = -1/√2

3x=±arccos(-1/√2) + 2πn

3x= ±3/4 π + 2πn

x= ±π/4 + 2/3 πn, где n∈Z                                                                                            

Answer 2

To solve the equation cos(3x) = -1/√2, we'll need to find the values of x that satisfy this equation. Let's go step by step:

Step 1: Find the angle whose cosine is -1/√2. The cosine function is negative in the second and third quadrants. In the second quadrant, the reference angle whose cosine is 1/√2 is π/4 radians or 45 degrees. However, since cos(3x) is negative, we need to find the angle in the third quadrant, which will be 180 degrees (π radians) minus the reference angle:

Angle in the third quadrant = π - (π/4) = 3π/4 radians or 135 degrees.

Step 2: Set 3x equal to the angle found in Step 1 and find the values of x.

3x = 3π/4

Step 3: Solve for x:

x = (3π/4) / 3 x = π/4 radians or 45 degrees.

So, the solutions to the equation cos(3x) = -1/√2 are x = π/4 radians and x = 45 degrees. However, keep in mind that trigonometric functions are periodic, so there are infinitely many solutions to this equation. The general solution for x can be written as:

x = (2nπ + π/4) radians or (90n + 45) degrees, where n is an integer.