Solve for all values of x:
sin3x = 1/2
To solve for all values of x in the equation `sin(3x) = 1/2`, we can use the inverse sine function, also called arcsine or sin^(-1), to find the possible angles.
The inverse sine function gives us the angle whose sine equals a given value. In this case, we need to find the angle whose sine is equal to 1/2.
Let's proceed with step-by-step instructions:
Step 1: Write the equation sin(3x) = 1/2.
Step 2: Apply the inverse sine function to both sides of the equation. The inverse sine of 1/2 is 30 degrees or π/6 radians. Therefore, we have:
3x = 30° + 360°n or 3x = π/6 + 2πn,
where n is an integer.
Step 3: Solve for x by dividing both sides of the equation by 3:
x = 10° + 120°n or x = π/18 + (2π/3)n,
where n is an integer.
So the solutions for x are all angles of the form 10° + 120°n or π/18 + (2π/3)n, where n is an integer.