Sin^-1(-1/2)
To find the value of sin^-1(-1/2), we need to determine the angle whose sine is equal to -1/2
To find the value of sin^-1(-1/2), we need to determine the angle whose sine is equal to -1/2. The inverse sine function, sin^-1, or arcsin, is defined such that sin^-1(x) gives the angle whose sine is x.
In this case, we want to find the angle whose sine is -1/2. Since the sine function has a periodicity of 2π, we can find multiple angles that satisfy this condition.
To make it easier, we will use the unit circle to find the angle. The unit circle is a circle with a radius of 1 centered at the origin (0, 0) in the Cartesian coordinate system. We can use this circle to define trigonometric functions for any angle.
The angle whose sine is -1/2 corresponds to the “stooping down” portion of the unit circle, where the y-coordinate is negative. In the fourth quadrant of the unit circle, we have an angle θ such that sin(θ) = -1/2.
To determine this angle, we can use the fact that sin(π/6) = 1/2. It means that π/6 and -π/6 yield sine values of 1/2. Since we want the negative value, we have -π/6 as a possible solution.
Therefore, the value of sin^-1(-1/2) is -π/6, or approximately -0.5236 radians.
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