What is the solution for sin(x) = -1 between 0° and 360°?

The solution for sin(x) = -1 between 0° and 360° is x = 270°.

To understand why, let's first recall that the sine function, sin(x), represents the y-coordinate of a point on the unit circle. The unit circle is a circle with a radius of 1, centred at the origin of a coordinate plane. As you move around the circle, the sine of an angle corresponds to the vertical distance from the x-axis to the point on the circle.

The sine function reaches its minimum value of -1 at a specific point on the unit circle. This occurs when the angle x is 270°, which is directly downward from the centre of the circle. At this point, the y-coordinate is -1, and thus sin(270°) = -1.

To find this solution, you can also use the properties of the sine function. The sine function is periodic with a period of 360°, meaning it repeats its values every 360°. Within one full cycle from 0° to 360°, the sine function reaches -1 only once, at 270°.

Therefore, the only angle between 0° and 360° where sin(x) = -1 is at x = 270°. This is a key point to remember when solving trigonometric equations involving the sine function within a specified interval.