Question

Sin(3x/5+П/3)=корень из 3 на 2.

Answer 1

Решение дано на фото.

Answer 2

To solve the equation sin(3x/5 + π/3) = √3/2, we'll follow these steps:

Step 1: Identify the general form of the equation. Step 2: Apply the inverse trigonometric function to both sides. Step 3: Solve for x. Step 4: Check for extraneous solutions.

Step 1: General form of the equation is sin(θ) = √3/2.

Step 2: Apply the inverse trigonometric function, which is arcsin, to both sides:

arcsin(sin(3x/5 + π/3)) = arcsin(√3/2).

Step 3: Simplify and solve for x:

Since sin(arcsin(θ)) = θ (the arcsin function undoes the sin function), we have:

3x/5 + π/3 = π/3

Now, isolate x:

3x/5 = 0

x = 0.

Step 4: Check for extraneous solutions:

We must check if x = 0 is a valid solution in the original equation:

sin(3(0)/5 + π/3) = sin(0 + π/3) = sin(π/3) = √3/2.

The original equation holds true for x = 0, so it is indeed a valid solution.

Thus, the solution to the equation sin(3x/5 + π/3) = √3/2 is x = 0.