Verify the Identity 2sin(x)+1=0

Problem

2*sin(x)+1=0

Solution

1. Isolate the trigonometric term by subtracting 1 from both sides of the equation.

2*sin(x)=−1

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

sin(x)=−1/2

3. Identify the reference angle where the sine value is 1/2 which is π/6 or 30

sin(π/6)=1/2

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

Quadrant III: *x=π+π/6=(7*π)/6

Quadrant IV: *x=2*π−π/6=(11*π)/6

5. Generalize the solution by adding multiples of the period 2*π to account for all possible angles.

x=(7*π)/6+2*n*π

x=(11*π)/6+2*n*π

Final Answer

x=(7*π)/6+2*n*π,(11*π)/6+2*n*π

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