Answer:
The value of sin^-1(-3√2) is an angle whose sine is -3√2.
Since the sine function is an odd function, sin(-θ) = -sin(θ), we can find the reference angle by taking the inverse sine of the positive value 3√2, which gives:
sin^-1(3√2) ≈ 80.06°
The sine function is also negative in the third and fourth quadrants of the unit circle. Since the given value is negative, the angle must lie in either the third or fourth quadrant.
To determine in which quadrant the angle lies, we can use the fact that sine is negative in the third and fourth quadrants. Since sin^-1(-3√2) gives a positive value, the angle must lie in the third quadrant where the sine is negative.
Therefore, sin^-1(-3√2) = -80.06° (rounded to two decimal places).
Explanation: