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 270 or (3*π)/2 radians, plus any integer multiple of 2*π

sin(θ)=−1⇒θ=(3*π)/2+2*k*π

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

2*x=(3*π)/2+2*k*π

3. Solve for x by dividing the entire equation by 2

x=(3*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=(3*π)/4+k*π

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