Question

Решить sin 6 x= 1/2

Answer 1

Ответ: x=5

Пошаговое объяснение:sin 30 =1/2

=> 6*x=30=>x = 30 / 6 = 5

Answer 2

To solve the equation sin(6x) = 1/2, you need to find the values of x that satisfy the equation. Here's how you can do it:

Step 1: Find the reference angle for sin^(-1)(1/2): The reference angle for sin^(-1)(1/2) is π/6 radians or 30 degrees.

Step 2: Determine the solutions in the interval [0, 2π): Since the sine function has a periodicity of 2π, you can find the solutions by setting up the equation:

6x = π/6 + 2πn or 6x = 5π/6 + 2πn

where n is an integer (positive, negative, or zero) to account for all possible solutions.

Step 3: Solve for x: a) For the first equation, π/6 + 2πn:

Divide both sides by 6: x = (π/6 + 2πn) / 6

b) For the second equation, 5π/6 + 2πn:

Divide both sides by 6: x = (5π/6 + 2πn) / 6

These are the general solutions for x in the interval [0, 2π) that satisfy sin(6x) = 1/2.

Step 4: Find specific solutions in the interval [0, 2π):

To get the specific solutions, plug in different integer values for n and calculate the corresponding values of x. Remember that you want solutions within the interval [0, 2π).

Let's find the first few values of x:

For n = 0: x = (π/6 + 2π * 0) / 6 = π/36

For n = 1: x = (π/6 + 2π * 1) / 6 = 7π/36

For n = 2: x = (π/6 + 2π * 2) / 6 = 13π/36

For n = 3: x = (π/6 + 2π * 3) / 6 = 19π/36

For n = 4: x = (π/6 + 2π * 4) / 6 = 25π/36

For n = 5: x = (π/6 + 2π * 5) / 6 = 31π/36

Make sure to keep adding multiples of 2π to find other solutions if needed. These are some of the solutions for x that satisfy the equation sin(6x) = 1/2 in the interval [0, 2π).