Questions: Algebra 2 Sem2 Quiz 2.2.1 - The Unit Circle Value: 3 Use the Unit Circle to find the exact value of the inverse trig function. Remember that the domain of inverse sine is limited to quadrants I and IV (the right side of the unit circle) sin^(-1)(-1/2) ○ a. 30° ○ b. 240° - c. 330° - d. 0°

Solution Steps

The problem asks for the value of $\sin^{-1}(\frac{1}{2})$ within the specified domain.

On the unit circle, the sine of an angle corresponds to the y-coordinate. We are looking for an angle whose sine is $\frac{1}{2}$. Since the domain of inverse sine is limited to quadrants I and IV, we consider only the right half of the unit circle.

In quadrant I, the angle whose sine is $\frac{1}{2}$ is $30^\circ$ or $\frac{\pi}{6}$ radians. In quadrant IV, there's no angle with a positive sine value. Therefore, $\sin^{-1}(\frac{1}{2}) = 30^\circ$.

Final Answer: The final answer is $\boxed{30^\circ}$