Find the values of x that satisfy the equation 3sin(x) - 2 = 0.

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Question: Find the values of x that satisfy the equation 3sin(x) - 2 = 0.

Options:

Correct Answer: π/2

Solution:

The solution is x = π/2.

Find the values of x that satisfy the equation 3sin(x) - 2 = 0.

Find the values of x that satisfy the equation 3sin(x) - 2 = 0.

Step 1: Start with the equation 3sin(x) - 2 = 0.
Step 2: Add 2 to both sides of the equation to isolate the sine term: 3sin(x) = 2.
Step 3: Divide both sides by 3 to solve for sin(x): sin(x) = 2/3.
Step 4: Use the inverse sine function to find x: x = arcsin(2/3).
Step 5: Calculate the value of arcsin(2/3) to find the principal value of x.
Step 6: Remember that sine is positive in the first and second quadrants, so find the second solution: x = π - arcsin(2/3).
Step 7: The general solutions can be expressed as x = arcsin(2/3) + 2kπ and x = π - arcsin(2/3) + 2kπ, where k is any integer.

Trigonometric Equations – The question tests the ability to solve a basic trigonometric equation involving the sine function.
Inverse Functions – It requires understanding how to apply the inverse sine function to find the angle corresponding to a given sine value.