Verify the Identity 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 (3*π)/2 and every full rotation thereafter.

sin(θ)=−1⇒θ=(3*π)/2+2*π*n

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

3*x=(3*π)/2+2*π*n

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

x=((3*π)/2+2*π*n)/3

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

x=π/2+(2*π*n)/3

Final Answer

sin(3*x)=−1⇒x=π/2+(2*π*n)/3

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