Solve: 2 sin x - 1 = 0 for 0 degrees is less than or equal to x is less than 360 degrees.
Look for the x values for which
sin x = 0.5.
x will have to be in the first or second quadrant, for the sine to be positive. There will be two possible answers.
To solve the equation 2 sin x - 1 = 0 for 0 degrees ≤ x < 360 degrees, you can follow these steps:
Step 1: Add 1 to both sides of the equation:
2 sin x = 1
Step 2: Divide both sides of the equation by 2:
sin x = 1/2
Step 3: Find the reference angle:
Since sin(x) = 1/2, we know that x lies in the first and second quadrants of the unit circle. The reference angle is the angle that has the same sine value in the first quadrant. The reference angle for sin^(-1)(1/2) is 30 degrees or π/6 radians.
Step 4: Identify the values of x:
We need to find all the values of x in the range of 0 degrees ≤ x < 360 degrees that have a sine value of 1/2. In the first quadrant, the value of sin(x) = 1/2 at 30 degrees or π/6 radians. In the second quadrant, the sine function is also positive, so there is another angle that satisfies the equation: 180 - 30 = 150 degrees.
Step 5: Write the solutions:
x = 30 degrees, 150 degrees (or x = π/6 radians, 5π/6 radians) are the solutions to the equation 2 sin x - 1 = 0 for 0 degrees ≤ x < 360 degrees.
To solve the equation 2 sin(x) - 1 = 0, we can follow these steps:
Step 1: Add 1 to both sides of the equation to isolate the "sin(x)" term:
2 sin(x) = 1
Step 2: Divide both sides of the equation by 2 to solve for "sin(x)":
sin(x) = 1/2
Now, to find the values of x that satisfy this equation, we need to look at the unit circle or use a calculator.
On the unit circle, sin(x) gives the y-coordinate of the point where the angle x intersects the unit circle. We are looking for angles whose sin values are 1/2.
The unit circle shows two angles where sin(x) = 1/2, which are 30 degrees and 150 degrees. However, as per the given condition of 0 degrees ≤ x < 360 degrees, we need to include all possible angles that satisfy the equation.
So, the values of x can be x = 30 degrees and x = 150 degrees.
Therefore, the solution to the equation 2 sin(x) - 1 = 0 for 0 degrees ≤ x < 360 degrees is x = 30 degrees and x = 150 degrees.