Solve for x sin(2x)=1

Problem

sin(2*x)=1

Solution

1. Identify the general solution for the sine function when it equals 1. The sine of an angle is 1 when the angle is π/2 plus any integer multiple of 2*π

sin(θ)=1⇒θ=π/2+2*k*π

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

2*x=π/2+2*k*π

3. Solve for x by dividing both sides of the equation by 2.

x=π/4+k*π

4. Define the variable k as any integer to represent the infinite set of solutions.

k∈ℤ

Final Answer

sin(2*x)=1⇒x=π/4+k*π,k∈ℤ

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