Solve for x sin(x)=1/4

Problem

sin(x)=1/4

Solution

1. Identify the equation as a basic trigonometric equation of the form sin(x)=a where a is within the range [−1,1]

2. Apply the inverse sine function to find the principal value, often called the arcsine.

x=arcsin(1/4)

3. Determine the general solution for the first quadrant and second quadrant, as the sine function is positive in both.

x=arcsin(1/4)+2*π*n

x=π−arcsin(1/4)+2*π*n

4. Define the integer constant n to represent all possible coterminal angles in the general solution.

n∈ℤ

Final Answer

sin(x)=1/4⇒x=arcsin(1/4)+2*π*n,π−arcsin(1/4)+2*π*n

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