Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. sin(theta)=-(1)/(2)

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Solve the given equation. (Enter your answers as a comma-separated list. Let  k be any integer.  sin(theta)=-(1)/(2)

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Identify Sine Value: The equation sin(theta) = -(1)/(2) implies that theta is an angle whose sine is -1/2. We know that the sine function has a value of -1/2 at specific angles in the third and fourth quadrants of the unit circle, where the sine values are negative.Find Reference Angle: The reference angle for which the sine has a value of 1/2 is 30 degrees or pi/6 radians. In the third and fourth quadrants, we need to find the angles that have this reference angle but with a negative sine value.Third Quadrant Angle: In the third quadrant, the angle with a sine of -1/2 is 180 degrees + 30 degrees, which is 210 degrees or in radians, pi + pi/6, which simplifies to (7pi)/6.Fourth Quadrant Angle: In the fourth quadrant, the angle with a sine of -1/2 is 360 degrees - 30 degrees, which is 330 degrees or in radians, 2pi - pi/6, which simplifies to (11pi)/6.General Solutions: Since the sine function is periodic with a period of 2pi, we can add any integer multiple of 2pi to our solutions to get the general form of the solutions. Therefore, the general solutions are (7pi)/6 + 2kpi and (11pi)/6 + 2kpi, where k is any integer.

Solve the given equation. (Enter your answers as a comma-separated list. Let $k$ be any integer. $\newline$ $\sin(\theta) = -\frac{1}{2}$

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Solve the given equation. (Enter your answers as a comma-separated list. Let $k$ be any integer. $\newline$ $\sin(\theta) = -\frac{1}{2}$