Solve for x square root of 2sin(x)+1=0

Problem

√(,2*sin(x)+1)=0

Solution

1. Square both sides to eliminate the radical.

√(,2*sin(x)+1)2=0

2*sin(x)+1=0

2. Isolate the sine term by subtracting 1 from both sides and then dividing by 2.

2*sin(x)=−1

sin(x)=−1/2

3. Find the reference angle for the equation.

sin(θ)=1/2⇒θ=π/6

4. Determine the quadrants where the sine function is negative, which are Quadrant III and Quadrant IV.

x=π+π/6=(7*π)/6

x=2*π−π/6=(11*π)/6

5. State the general solution by adding multiples of the period 2*π

x=(7*π)/6+2*π*n

x=(11*π)/6+2*π*n

Final Answer

√(,2*sin(x)+1)=0⇒x=(7*π)/6+2*π*n,(11*π)/6+2*π*n

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