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Welcome to **arcctg -(2+√3)**, our post aboutthe arccotangent of -(2+√3).

For the inverse trigonometric function of cotangent -(2+√3) we usually employ the abbreviation *arcctg* and write it as arcctg -(2+√3) or arcctg(-(2+√3)).

If you have been looking for *what is arcctg -(2+√3)*, either in degrees or radians, or if you have been wondering about the inverse of ctg -(2+√3), then you are right here, too.

In this post you can find the angle arccotangent of -(2+√3), along with identities.

Read on to learn all about the arcctg of -(2+√3), and note that the term -2-√3 is approximately -3.7320508 as a decimal number.

## Arcctg of -(2+√3)

If you want to know *what is arcctg -(2+√3)* in terms of trigonometry, check out the explanations in the last paragraph; ahead in this section is the value of arccotangent(-(2+√3)):

arccotangent -(2+√3) = 11pi/12 rad = 165 °

arccotangent of -(2+√3) = 11pi/12 radians = 165 degrees

The arcctg of -(2+√3) is 11pi/12 radians, and the value in degrees is 165°. To change the result from the unit radian to the unit degree multiply the angle by 180° / $\pi$ and obtain 165°.

Our results above contain fractions of pi for the results in radian, and are exact values otherwise. If you compute arcctg(-(2+√3)), and any other angle, using the calculator below, then the value will be rounded to ten decimal places.

To obtain the angle in degrees insert -(2+√3) as decimal in the field labelled “x”. However, if you want to be given the angle of ctg -(2+√3) in radians, then you must press the swap units button.

### Calculate arcctg x

The identities of arccotangent -(2+√3) are as follows: arcctg(-(2+√3)) =

- $\frac{\pi}{2}$ – arctg(-(2+√3)) ⇔ 90°- arctg(-(2+√3))
- $\pi$ – arcctg((2+√3)) ⇔ 180°- arctg((2+√3))
- arctg(1/-(2+√3)) + $\pi $

The infinite series of arcctg -(2+√3) is: $\frac{\pi}{2}$ – $\sum_{n=0}^{\infty} \frac{(-1)^{n}(-(2+\sqrt{3}))^{2n+1}}{(2n+1)}$.

Next, we discuss the derivative of arcctg -(2+√3) for x = -(2+√3). In the following paragraph you can additionally learn what the search calculations form in the sidebar is used for.

## Derivative of arcctg -(2+√3)

The derivative of arcctg -(2+√3) is particularly useful to calculate the inverse cotangent -(2+√3) as an integral.

The formula for x is (arcctg x)’ = – $\frac{1}{1 + x^{2}}$, x ≠ -1,1, so for x = -(2+√3) the derivative equals -0.0669872981.

Using the arcctg -(2+√3) derivative, we can calculate the angle as a definite integral:

arcctg -(2+√3) = $\frac{\pi}{2}$ – $\int_{-(2+\sqrt{3})}^{\infty}\frac{1}{{1+z^{2}}}dz$.

The relationship of arcctg of -(2+√3) and the trigonometric functions sin, cos and tg is:

- sin(arccotangent(-(2+√3))) = $\frac{1}{\sqrt{1 + (-(2+\sqrt{3}))^{2}}}$
- cos(arccotangent(-(2+√3))) = $\frac{-(2+\sqrt{3})}{\sqrt{1 + (-(2+\sqrt{3}))^{2}}}$
- tg(arccotangent(-(2+√3))) = 1/-(2+√3)

Note that you can locate many terms including the arccotangent(-(2+√3)) value using the search form. On mobile devices you can find it by scrolling down. Enter, for instance, arcctg-(2+√3) angle.

Using the aforementioned form in the same way, you can also look up terms including derivative of inverse cotangent -(2+√3), inverse cotangent -(2+√3), and derivative of arcctg -(2+√3), just to name a few.

In the next part of this article we discuss the trigonometric significance of arccotangent -(2+√3), and there we also explain the difference between the inverse and the reciprocal of ctg -(2+√3).

## What is arcctg -(2+√3)?

In a triangle which has one angle of 90 degrees, the sine of the angle α is the ratio of the length of the opposite side o to the length of the hypotenuse h: sin α = o/h, and the cosine of the angle α is the ratio of the length of the adjacent side a to the length of the hypotenuse h: cos α = a/h.

In a circle with the radius r, the horizontal axis x, and the vertical axis y, α is the angle formed by the two sides x and r; r moving counterclockwise defines the positive angle.

As follows from the unit-circle definition on our homepage, assumed r = 1, in the intersection of the point (x,y) and the circle, sin α = y / r = y, cos α = x / r = x, and ctg α = x / y = -(2+√3). The angle whose cotangent value equals -(2+√3) is α.

In the interval ]0, pi[ or ]0°, 180°[, there is only one α whose arccotangent value equals -(2+√3). For that interval we define the function which determines the value of α as

From the definition of arcctg(-(2+√3)) follows that the *inverse* function y^{-1} = ctg(y) = -(2+√3). Observe that the *reciprocal* function of ctg(y),(ctg(y))^{-1} is 1/ctg(y).

Avoid misconceptions and remember (ctg(y))^{-1} = 1/ctg(y) ≠ ctg^{-1}(y) = arcctg(-(2+√3)). And make sure to understand that the trigonometric function y=arcctg(x) is defined on a restricted domain, where it evaluates to a single value only, called the principal value:

In order to be injective, also known as one-to-one function, y = arcctg(x) if and only if ctg y = x and 0 < y < pi. The domain of x is $\mathbb{R}$.

## Conclusion

The frequently asked questions in the context include *what is arcctg -(2+√3) degrees* and *what is the inverse cotangent -(2+√3)* for example; reading our content they are no-brainers.

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