Solve for x sin(2x-pi/2)=-1

Problem

sin(2*x−π/2)=−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 of the form (3*π)/2+2*k*π for any integer k

2*x−π/2=(3*π)/2+2*k*π

2. Isolate the term containing x by adding π/2 to both sides of the equation.

2*x=(3*π)/2+π/2+2*k*π

3. Simplify the constant terms on the right side.

2*x=2*π+2*k*π

4. Divide the entire equation by 2 to solve for x

x=π+k*π

5. Factor the expression to write the solution in a more compact form.

x=(k+1)*π

6. Generalize the result. Since k is any integer, k+1 is also any integer, which we can represent simply as n

x=n*π

Final Answer

sin(2*x−π/2)=−1⇒x=n*π

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