Question

Sin(x/4-п/3)=-корень из 3/2​

Answer 1

Ответ:

решение смотри на фотографии

Answer 2

To solve the equation sin(x/4 - π/3) = -√3/2, we can follow these steps:

Step 1: Simplify the equation: sin(x/4 - π/3) = -√3/2

Step 2: Identify the reference angle: The reference angle in this case is π/3. We need to find the angle within one full revolution that has the same sine value as -√3/2.

Step 3: Find the angle for the reference angle: The sine of π/3 is √3/2. Since the equation has a negative sine value, we need to find the angle in the third and fourth quadrants where the sine is -√3/2.

Step 4: Solve for x in the third and fourth quadrants: In the third quadrant, the angle is (π - π/3) = 2π/3. In the fourth quadrant, the angle is (-π/3 + 2π) = (5π/3).

Step 5: General solution: Since sine is a periodic function, we can add multiples of the period (2π) to the angles we found in step 4 to obtain the general solution.

Therefore, the general solution is: x = 2π/3 + 2πn, where n is an integer. x = 5π/3 + 2πn, where n is an integer.

These equations represent all the possible values of x that satisfy the given equation.