The inverse sine function, also known as arcsine, is denoted as sin-1(x) or arcsin(x). To find the inverse sine of 1/2, we are looking for an angle θ such that:
sin(θ) = 1/2In the unit circle, the sine of an angle refers to the y-coordinate of the point where the terminal side of the angle intersects the circle. The sine function is positive in the first and second quadrants. Therefore, we need to consider the angles whose sine value equals 1/2.
The angle whose sine is 1/2 is 30° (or π/6 radians) in the first quadrant. Additionally, in the second quadrant, the corresponding angle is 150° (or 5π/6 radians).
However, when we refer to the inverse sine function, it typically returns results within the interval [-π/2, π/2] (or [-90°, 90°]). Thus, the principal value of the inverse sine of 1/2 is:
sin-1(1/2) = π/6 (or 30°)In conclusion, when you’re tasked with finding sin-1(1/2), the answer is π/6 or 30°.