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Solve the equation for solutions in the interval sin 4x = V3/2

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Explanation:

To solve the equation sin(4x) = √(3/2), we can start by finding the values of x within the given interval [0, 2π], which is one full period of the sine function.

First, let's find the reference angle for sin(4x) = √(3/2). The reference angle for sin is π/3 since sin(π/3) = √(3/2).

Now, we can find the solutions within the interval [0, 2π] by considering the values of 4x:

1. 4x = π/3

2. 4x = 2π - π/3

Now, solve for x:

1. x = (π/3) / 4

x = π/12

2. x = (2π - π/3) / 4

x = (6π/3 - π/3) / 4

x = (5π/3) / 4

x = (5π/12)

So, the solutions for sin(4x) = √(3/2) in the interval [0, 2π] are x = π/12 and x = 5π/12.

Hopefully this helps you!! :)⋆˙⟡♡⟡⋆˙

User Martin Prazak
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