Final answer:
The values of sinx that satisfy the equation 4sin²x-3=0 on the interval [0,2π) are ±√3/2.
Step-by-step explanation:
To find the values of x that satisfy the equation 4sin²x-3=0 on the interval [0,2π), we need to isolate sin²x and then solve for x.
Step 1: Add 3 to both sides of the equation to get: 4sin²x = 3
Step 2: Divide both sides of the equation by 4 to get: sin²x = 3/4
Step 3: Take the square root of both sides of the equation to get: sinx = ±√(3/4)
Step 4: Simplify the square root to get: sinx = ±√3/2
So, the values of sinx that satisfy the equation are ±√3/2.