Find the values of x that satisfy 3sin(x) - 1 = 0.

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Question: Find the values of x that satisfy 3sin(x) - 1 = 0.

Options:

Correct Answer: π/6

Solution:

The solution is x = π/6 + 2nπ.

Find the values of x that satisfy 3sin(x) - 1 = 0.

Find the values of x that satisfy 3sin(x) - 1 = 0.

Step 1: Start with the equation 3sin(x) - 1 = 0.
Step 2: Add 1 to both sides of the equation to isolate the sine term: 3sin(x) = 1.
Step 3: Divide both sides by 3 to solve for sin(x): sin(x) = 1/3.
Step 4: Use the inverse sine function to find the angle x: x = arcsin(1/3).
Step 5: Since sine is positive in the first and second quadrants, find the two angles: x = arcsin(1/3) and x = π - arcsin(1/3).
Step 6: The general solutions for sine are given by: x = arcsin(1/3) + 2nπ and x = π - arcsin(1/3) + 2nπ, where n is any integer.
Step 7: For simplicity, we can express the first solution as x = π/6 + 2nπ, where n is any integer.

Trigonometric Equations – The question tests the ability to solve a basic trigonometric equation involving the sine function.
Periodic Solutions – It assesses understanding of the periodic nature of the sine function and how to express general solutions.