Solve for x sin(x)=5/13

Problem

sin(x)=5/13

Solution

1. Identify the inverse trigonometric function needed to isolate x which is the arcsine function.

2. Apply the arcsine function to both sides of the equation to find the principal value.

x=arcsin(5/13)

3. Account for the periodic nature of the sine function, noting that sin(π−θ)=sin(θ)

x=π−arcsin(5/13)

4. Generalize the solution by adding 2*π*n to both cases, where n is any integer, to represent all possible angles.

x=arcsin(5/13)+2*π*n

x=π−arcsin(5/13)+2*π*n

Final Answer

x=arcsin(5/13)+2*π*n,π−arcsin(5/13)+2*π*n

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