Question

Sin2x=-1/2 Help me please

Answer 1

Ответ:

2x=7π/6                                 2x=11π/6

2x=7π/6+2kπ, k∈Z                2x=11π/6+2kπ, k∈Z

x=7π/12+kπ, k∈Z                    x=11π/12+kπ, k∈Z

Объяснение:

Answer 2

To solve the equation sin(2x) = -1/2, you can follow these steps:

1. Find the reference angle: First, determine the reference angle for which sin(theta) = 1/2. This reference angle can be found using the unit circle or by using inverse trigonometric functions. In this case, sin(theta) = 1/2 when theta is 30 degrees or pi/6 radians.

2. Use the periodicity of sine: Remember that the sine function has a period of 2π, which means it repeats every 360 degrees or 2π radians. To find all solutions, you can add multiples of the period to the reference angle.

3. Set up the equation: You have sin(2x) = -1/2, and you know that sin(30 degrees) = 1/2. So, you need to find the values of 2x that are equivalent to 30 degrees plus multiples of 360 degrees.

4. Solve for x: Set up the equation: 2x = 30 degrees + 360 degrees * n where n is an integer representing the number of full cycles around the unit circle.

Now, solve for x:

For n = 0: 2x = 30 degrees x = 15 degrees

For n = 1: 2x = 30 degrees + 360 degrees * 1 2x = 390 degrees x = 195 degrees

These are the solutions for x in degrees. If you want the solutions in radians, you can convert them by using the fact that π radians is equivalent to 180 degrees:

For x = 15 degrees: x = 15 degrees * (π/180) = π/12 radians

For x = 195 degrees: x = 195 degrees * (π/180) = 13π/12 radians

So, the solutions for sin(2x) = -1/2 are: x = π/12 + 2πn x = 13π/12 + 2πn where n is an integer. These solutions cover all possible values of x that satisfy the equation.