Solve for x sin(x)=3/5

Problem

sin(x)=3/5

Solution

1. Identify the equation as a basic trigonometric equation where the sine of an angle x is a positive constant.

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

x=arcsin(3/5)

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

x=arcsin(3/5)+2*π*n

x=π−arcsin(3/5)+2*π*n

4. Define the integer constant n which represents any integer, accounting for the periodicity of the sine function.

n∈ℤ

Final Answer

sin(x)=3/5⇒x=arcsin(3/5)+2*π*n,π−arcsin(3/5)+2*π*n

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