Question

Помогите решить тригонометрические уравнения √3tgx-3≤0 2cosx+√3≥0 Срочно пожалуйста

Answer 1

Пошаговое объяснение:

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Answer 2

Solving Trigonometric Equations

To solve the trigonometric equations √3tg(x) - 3 ≤ 0 and 2cos(x) + √3 ≥ 0, we will break down the process step by step.

Step 1: Simplify the Equations

Let's simplify the equations to make them easier to work with.

For the first equation, √3tg(x) - 3 ≤ 0, we can rewrite it as:

√3tan(x) - 3 ≤ 0

For the second equation, 2cos(x) + √3 ≥ 0, we don't need to make any changes.

Step 2: Solve the First Equation

To solve the equation √3tan(x) - 3 ≤ 0, we need to isolate the variable x.

Add 3 to both sides of the equation:

√3tan(x) ≤ 3

Next, divide both sides of the equation by √3:

tan(x) ≤ 3/√3

Simplify the right side of the equation:

tan(x) ≤ √3

Now, we need to find the values of x that satisfy this inequality. We can use the unit circle or a calculator to find the values of x for which the tangent function is less than or equal to √3.

The solutions to the inequality tan(x) ≤ √3 are:

x ≤ π/3 + nπ, where n is an integer

Step 3: Solve the Second Equation

To solve the equation 2cos(x) + √3 ≥ 0, we need to isolate the variable x.

Subtract √3 from both sides of the equation:

2cos(x) ≥ -√3

Next, divide both sides of the equation by 2:

cos(x) ≥ -√3/2

Now, we need to find the values of x that satisfy this inequality. We can use the unit circle or a calculator to find the values of x for which the cosine function is greater than or equal to -√3/2.

The solutions to the inequality cos(x) ≥ -√3/2 are:

x ≥ 5π/6 + 2nπ or x ≤ 7π/6 + 2nπ, where n is an integer

Step 4: Combine the Solutions

To find the values of x that satisfy both equations, we need to find the intersection of the solution sets from Step 2 and Step 3.

The values of x that satisfy both equations are:

x ≤ π/3 + nπ, where n is an integer, and x ≥ 5π/6 + 2nπ or x ≤ 7π/6 + 2nπ, where n is an integer.

In other words, x can take on any value that satisfies both the inequality tan(x) ≤ √3 and the inequality cos(x) ≥ -√3/2.

I hope this helps! Let me know if you have any further questions.