Solve for x sin(x)=3/4

Problem

sin(x)=3/4

Solution

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

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

x=arcsin(3/4)

3. Determine the general solution for x in radians, accounting for the periodicity of the sine function (2*π*n and the identity sin(π−θ)=sin(θ)

x=arcsin(3/4)+2*π*n

x=π−arcsin(3/4)+2*π*n

4. Specify the domain for the integer n which represents any integer.

n∈ℤ

Final Answer

sin(x)=3/4⇒x=arcsin(3/4)+2*π*n,π−arcsin(3/4)+2*π*n

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