Solve for x sin(x)=8/17

Problem

sin(x)=8/17

Solution

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

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

x=arcsin(8/17)

3. Determine the general solution by accounting for the periodicity of the sine function, which repeats every 2*π radians, and the identity sin(π−θ)=sin(θ)

x=arcsin(8/17)+2*π*n

x=π−arcsin(8/17)+2*π*n

4. State the constraint for the integer n which represents any whole number of rotations.

n∈ℤ

Final Answer

sin(x)=8/17⇒x=arcsin(8/17)+2*π*n,π−arcsin(8/17)+2*π*n

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