4sin^(2)x-3=0

To solve the equation 4sin^(2)x - 3 = 0, we can follow these steps:

Step 1: Isolate the sine term
Add 3 to both sides:
4sin^(2)x - 3 + 3 = 0 + 3
4sin^(2)x = 3

Step 2: Divide both sides by 4
Divide both sides by 4 to solve for sin^(2)x:
(4sin^(2)x) / 4 = 3 / 4
sin^(2)x = 3 / 4

Step 3: Take the square root of both sides
To solve for sin x, take the square root of both sides:
√(sin^(2)x) = √(3 / 4)
|sin x| = √3 / 2

Step 4: Find the values of sin x
Since we squared the sin x term, we need to consider both the positive and negative square roots.
- sin x = √3 / 2 or sin x = √3 / 2

Step 5: Find the angle values
To find the values of x, we can use the inverse sine function. In this case, we are looking for angles where the sine is either √3 / 2 or -√3 / 2.
The angles where sin x = √3 / 2 are π/3 and 2π/3 in the first and second quadrants.
The angles where sin x = -√3 / 2 are 4π/3 and 5π/3 in the third and fourth quadrants.

So, the solutions to the equation 4sin^(2)x - 3 = 0 are:
x = π/3, 2π/3, 4π/3, 5π/3.