First, recall that the arctangent function, often written as atan or tan^-1, returns the inverse tangent of a number. In this case, we are asked to find the arctangent of -sqrt3. This requires a bit knowledge on the unit circle and understanding of the tangent function.
The tangent function, tan(θ), gives the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle in a right triangle. It is basically y-coordinate/x-coordinate (also known as sine over cosine).
Now, we find the point on the unit circle where the tangent equals -sqrt3. This happens at 120 degrees and 300 degrees. However, the tangent function is negative in the 2nd and 4th quadrants, so we can rule out 120 degrees. So, we're left with 300 degrees.
In trigonometry, angles are typically measured in terms of radians, not degrees. Therefore, you have to convert 300 degrees to radians.
Remember that:
180 degrees = π radians
300 degrees = 300*(π/180) radians = 5π/3 radians
In the context of the arctangent function, which only returns values from -(π/2) to (π/2) (or -90 degrees to 90 degrees), we have to make an adjustment. Given this principle, our angle falls outside this domain, so we need to subtract π (or 180 degrees) to get an equivalent angle within the domain.
Subtracting π from 5π/3 gives -π/3, which falls within the domain. Converting -π/3 radians to degrees, you get -60 degrees.
Therefore, the arctangent of -sqrt3 is -60 degrees (or -π/3 radians) when expressed in context of the standard range of the inverse trigonometric functions.