what is the inverse tangent of negative root3/3

let tan^-1 (-√3/3) = Ø

then tanØ = -√3/3

I know tan 30° or tan π/6 = +√3/3

Ø must be in quadrants II or IV

in degrees: Ø = 180-30=150° or Ø = 360-30 = 330°
in radians: Ø = π - π/6 = 5π/6 or Ø = 2π-π/6 = 11π/6

notice that your calculator gives you -30° or -π/6
which is correct since -30° is coterminal with 330°

calculators have been programmed to give the closest answer to zero, which in this case is -30°

the smallest positive answer is 5π/6

To find the inverse tangent of a value, you can use the inverse tangent function, usually denoted as `arctan` or `tan^(-1)`.

In this case, you want to find the inverse tangent of negative √3/3. The inverse tangent function takes an angle and returns the corresponding tangent value.

The tangent of an angle is defined as the ratio of the length of the leg opposite to the angle to the length of the leg adjacent to the angle in a right triangle.

Let's assume that the angle is θ. Then, we have:

tan(θ) = (-√3/3)

To find the angle θ, we need to take the inverse tangent (or arctangent) of both sides:

θ = arctan(-√3/3)

Using a calculator or math software that has an inverse tangent function, you can find the answer. Let me calculate it for you.

θ ≈ - π/6 radians or -30 degrees

Therefore, the inverse tangent of -√3/3 is approximately - π/6 radians or -30 degrees.