Solve for x sin(x)=3/5

Problem

sin(x)=3/5

Solution

1. Identify the equation as a basic trigonometric equation where you need to find the angle x whose sine is 3/5

2. Apply the inverse sine function to both sides of the equation to isolate x for the principal value.

x=arcsin(3/5)

3. Determine the general solution for x in radians, noting that the sine function is positive in the first and second quadrants.

x=arcsin(3/5)+2*π*n

x=π−arcsin(3/5)+2*π*n

4. Define the variable n as any integer to represent all possible coterminal angles.

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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