Solve for x sin(3x)=1

Problem

sin(3*x)=1

Solution

1. Identify the general solution for the sine function when it equals 1 The sine of an angle is 1 at π/2 and every full rotation thereafter.

sin(θ)=1⇒θ=π/2+2*n*π

2. Substitute the argument of the sine function, which is 3*x into the general solution formula.

3*x=π/2+2*n*π

3. Solve for x by dividing the entire equation by 3

x=(π/2+2*n*π)/3

4. Simplify the expression to find the final general solution for x where n is any integer.

x=π/6+(2*n*π)/3

Final Answer

sin(3*x)=1⇒x=π/6+(2*n*π)/3,n∈ℤ

Want more problems? Check here!