Question

Sin(2x-п/3)=корень 3/2​

Answer 1

Відповідь:

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Покрокове пояснення:

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Answer 2

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

1. Rewrite the right-hand side as a fraction: √3/2 = 1/2√3.

2. Recall the trigonometric identity sin(θ) = a/b, where θ is an angle and a/b is a fraction. This identity implies that the angle θ has a sine value of a/b.

3. In our equation sin(2x - π/3) = 1/2√3, we can compare it with the trigonometric identity. We have a/b = 1/2√3. This implies that a = 1 and b = 2√3.

4. Find the angle associated with the fraction a/b = 1/2√3. The angle whose sine is 1/2√3 is π/6.

5. Set the argument of sin(2x - π/3) equal to the angle π/6: 2x - π/3 = π/6.

6. Solve for x by isolating the variable. Add π/3 to both sides of the equation: 2x = π/6 + π/3.

7. Simplify the right-hand side: 2x = π/6 + 2π/6 = 3π/6 = π/2.

8. Divide both sides by 2: x = π/4.

Therefore, the solution to the equation sin(2x - π/3) = √3/2 is x = π/4.