Solve for x 4sin(x)^2-1=0

Problem

4*sin2(x)−1=0

Solution

1. Isolate the trigonometric term by adding 1 to both sides.

4*sin2(x)=1

2. Divide both sides by 4 to solve for the squared sine function.

sin2(x)=1/4

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

sin(x)=±√(,1/4)

sin(x)=±1/2

4. Identify the angles on the unit circle where the sine value is 1/2 or −1/2

sin(x)=1/2⇒x=π/6+2*n*π,(5*π)/6+2*n*π

sin(x)=−1/2⇒x=(7*π)/6+2*n*π,(11*π)/6+2*n*π

5. Consolidate the solutions into a more compact form if desired, noting that each solution is separated by π

x=π/6+n*π

x=(5*π)/6+n*π

Final Answer

x=π/6+n*π,(5*π)/6+n*π

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