Solve for x sin(x)=4/5

Problem

sin(x)=4/5

Solution

1. Identify the equation as a basic trigonometric equation where you need to find the angle x whose sine is 4/5

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

x=arcsin(4/5)

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

x=arcsin(4/5)+2*π*n

x=π−arcsin(4/5)+2*π*n

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

n∈ℤ

Final Answer

sin(x)=4/5⇒x=arcsin(4/5)+2*π*n,π−arcsin(4/5)+2*π*n

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