4sin^2x-1=0
Are the angles 30, 120, and 210 and 300?
To determine if the angles 30, 120, 210, and 300 satisfy the equation 4sin^2(x) - 1 = 0, we need to solve this equation.
Step 1: Start with the given equation: 4sin^2(x) - 1 = 0.
Step 2: Add 1 to both sides of the equation: 4sin^2(x) = 1.
Step 3: Divide both sides of the equation by 4: sin^2(x) = 1/4.
Step 4: Take the square root of both sides of the equation: sin(x) = ±√(1/4).
Step 5: Simplify the square root: sin(x) = ±1/2.
The sine function has values of ±1/2 at multiple angles. These values are 30 degrees, 150 degrees, 210 degrees, 330 degrees, and their corresponding angles in radian units. So, the angles 30 and 210 (and their corresponding angles in radian units) satisfy the equation sin(x) = ±1/2. However, the angles 120 and 300 (and their corresponding angles in radian units) do not satisfy the equation.
Therefore, the angles 30 and 210 (and their corresponding angles in radian units) satisfy the equation 4sin^2(x) - 1 = 0, while the angles 120 and 300 (and their corresponding angles in radian units) do not.