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

Problem

cos(2*x−π/2)=−1

Solution

1. Identify the general solution for the cosine function when it equals −1 The cosine of an angle is −1 when the angle is an odd multiple of π

cos(θ)=−1⇒θ=π+2*k*π

2. Substitute the expression inside the cosine function for θ where k is any integer.

2*x−π/2=π+2*k*π

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

2*x=π+π/2+2*k*π

4. Combine the constant terms on the right side.

2*x=(3*π)/2+2*k*π

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

x=(3*π)/4+k*π

Final Answer

cos(2*x−π/2)=−1⇒x=(3*π)/4+k*π

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