Solve for θ in Radians sin(theta)=-1/2

Problem

sin(θ)=−1/2

Solution

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

α=π/6

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

3. Calculate the general solution for Quadrant III using the formula θ=π+α+2*k*π

θ=π+π/6+2*k*π

θ=(7*π)/6+2*k*π

4. Calculate the general solution for Quadrant IV using the formula θ=2*π−α+2*k*π

θ=2*π−π/6+2*k*π

θ=(11*π)/6+2*k*π

Final Answer

θ=(7*π)/6+2*k*π,(11*π)/6+2*k*π

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