Question

3*arcctg(-(корень3)/3) =

Answer 1

$3*arcCtg(-\frac{\sqrt{3}}{3})=3*\frac{2\pi }{3}=2\pi$

Answer 2

To solve this trigonometric expression, let's break it down step by step.

The given expression is: 3 * arccot(-√3/3)

First, we need to find the angle whose cotangent is -√3/3. Cotangent is the reciprocal of the tangent function. The tangent of an angle can be defined as the ratio of the length of the side opposite the angle to the length of the adjacent side in a right triangle.

Let's consider a right triangle where the opposite side is √3 and the adjacent side is -1 (since it's negative). The cotangent of the angle θ is given by:

cot(θ) = adjacent / opposite cot(θ) = -1 / √3 cot(θ) = -√3/3

So, the given expression can be written as: 3 * arccot(-√3/3)

Now, we need to find the angle θ such that cot(θ) = -√3/3. We know that arccot(x) is the inverse function of cot(x), so if cot(θ) = -√3/3, then θ = arccot(-√3/3).

Using a calculator, you can find the approximate value of arccot(-√3/3) to be 150 degrees.

Finally, substitute the value of θ back into the expression: 3 * 150 3 * 150 = 450

So, 3 * arccot(-√3/3) is equal to 450 degrees.