Final answer:
The values of x for which sin(x) = -0.8176 in the given interval are approximately -55.56° and 304.44°.
Step-by-step explanation:
To find the values of x for which sin(x) = -0.8176 in the interval 0° ≤ x ≤ 360°, we can use the inverse sine function to solve for x.
The inverse sine function, also known as arcsine, can be used to find the angle whose sine is a given value.
Using a calculator, we can find that arcsin(-0.8176) ≈ -55.56°.
However, since the interval is restricted to 0° ≤ x ≤ 360°, we need to find the equivalent positive angle.
Since sine has a period of 360°, we can add 360° to the negative angle to find the positive angle:
-55.56° + 360° = 304.44°
Therefore, the values of x for which sin(x) = -0.8176 in the given interval are approximately -55.56° and 304.44°.