To evaluate the expression for the inverse sine of negative one, we need to determine the angle whose sine value equals negative one. The inverse sine function, denoted as sin-1(x)
, is defined for angles between -\frac{\pi}{2}
and \frac{\pi}{2}
. This range corresponds to the first and fourth quadrants of the unit circle.
In the first quadrant (from 0
to \frac{\pi}{2}
), all sine values are positive. Conversely, in the fourth quadrant (from -\frac{\pi}{2}
to 0
), sine values are negative. Since we are looking for the inverse sine of a negative value, our solution must lie in the fourth quadrant.
Specifically, we need to find the angle where the sine equals negative one. This occurs at -\frac{\pi}{2}
, where the sine function reaches its minimum value. Therefore, the solution to the expression sin-1(-1)
is:
-\frac{\pi}{2}
This result indicates that the angle corresponding to the sine of negative one is -90
degrees or -\frac{\pi}{2}
radians.