Solve for x sin(x)^2-1=0

Problem

sin(x)−1=0

Solution

1. Isolate the squared trigonometric term by adding 1 to both sides of the equation.

sin(x)=1

2. Take the square root of both sides, remembering to include both the positive and negative roots.

sin(x)=±√(,1)

sin(x)=±1

3. Identify the values of x where the sine function equals 1 or −1 on the unit circle.

sin(x)=1⇒x=π/2+2*n*π

sin(x)=−1⇒x=(3*π)/2+2*n*π

4. Combine the solutions into a single general expression, noting that the values occur at every odd multiple of π/2

x=π/2+n*π

Final Answer

sin(x)−1=0⇒x=π/2+n*π

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