What values of x satisfy the equation sin x = -1?

The equation sin x = -1 indicates that we are looking for values of x where the sine function takes the value of -1. The sine function corresponds to the y-coordinate on the unit circle, and it reaches -1 at specific points.

In the context of the unit circle, sin x = -1 occurs at an angle of 270 degrees. This is the angle where the point on the unit circle is at the lowest point (0, -1). Additionally, since the sine function has a periodic nature, it can be expressed in terms of its periodicity.

The sine function has a period of 360 degrees, meaning that if you take any angle where sin x = -1 and add or subtract multiples of 360 degrees, you will still be at a position where sin x = -1. Therefore, we can express the general solution as x = 270 + 360n, where n is any integer.

If we extend this definition, we can also consider angles that represent the same position but in different rotations. The choice of -90 degrees is interesting because adding 360 degrees to -90 gives us 270 degrees, therefore it can be seen as another way of stating the same location on the unit circle.

Thus