Solve for x sin(x)=-1/2

Problem

sin(x)=−1/2

Solution

1. Identify the reference angle by finding the value of θ such that sin(θ)=1/2 in the first quadrant.

θ=π/6

2. Determine the quadrants where the sine function is negative. Since sin(x)=−1/2 x must be in Quadrant III or Quadrant IV.

3. Calculate the general solution for Quadrant III using the reference angle.

x=π+π/6+2*k*π

x=(7*π)/6+2*k*π

4. Calculate the general solution for Quadrant IV using the reference angle.

x=2*π−π/6+2*k*π

x=(11*π)/6+2*k*π

5. State the solution where k is any integer.

Final Answer

x=(7*π)/6+2*k*π,(11*π)/6+2*k*π

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