Find all angles, 0, degrees, is less than or equal to, theta, is less than, 360, degrees0 ∘ ≤θ<360 ∘ , that solve the following equation.sine, theta, equals, minus, one halfsinθ=− 21
Question
Find all angles, 0, degrees, is less than or equal to, theta, is less than, 360, degrees0 ∘ ≤θ<360 ∘ , that solve the following equation.sine, theta, equals, minus, one halfsinθ=− 21
Solution
The given equation is sinθ = -1/2.
The sine function is negative in the third and fourth quadrants.
In the unit circle, sinθ = -1/2 corresponds to an angle of 30 degrees below the x-axis.
So, the solutions in the third and fourth quadrants are:
Third quadrant: θ = 180 + 30 = 210 degrees Fourth quadrant: θ = 360 - 30 = 330 degrees
So, the solutions to the equation sinθ = -1/2 in the interval 0 ≤ θ < 360 are θ = 210 degrees and θ = 330 degrees.
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