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!! :)⋆˙⟡♡⟡⋆˙