Step-by-step explanation:
The exact value of sin^-1(-√2/2) in radians, in terms of π, is -π/4.
Here's how we arrive at this answer:
1. Recall that sin^-1(x) represents the inverse sine function, also known as arcsine. It asks, "What angle has a sine value of x?"
2. We need to find an angle whose sine is -√2/2.
3. Remembering the unit circle, we know that the sine value is -√2/2 at an angle of -π/4.
4. Therefore, sin^-1(-√2/2) = -π/4.
Key points:
- The negative sign in -√2/2 indicates that the angle is in the fourth quadrant, where sine is negative.
- The angle -π/4 is a standard angle on the unit circle, and its sine value is indeed -√2/2.
I hope this explanation is helpful!
