Table of Contents

Welcome to arccot 2 + sqrt3, our post aboutthe arccotangent of 2 + sqrt3.

For the inverse trigonometric function of cotangent 2 + sqrt3 we usually employ the abbreviation *arccot* and write it as arccot 2 + sqrt3 or arccot(2 + sqrt3).

If you have been looking for *what is arccot 2 + sqrt3*, either in degrees or radians, or if you have been wondering about the inverse of cot 2 + sqrt3, then you are right here, too.

In this post you can find the angle arccotangent of 2 + sqrt3, along with identities.

Read on to learn all about the arccot of 2 + sqrt3, and note that the term 2+sqrt3 is approximately 3.732050807 as a decimal number.

## Arccot of 2 + sqrt3

If you want to know *what is arccot 2 + sqrt3* in terms of trigonometry, check out the explanations in the last paragraph; ahead in this section is the value of arccotangent(2 + sqrt3):

arccotangent 2 + sqrt3 = pi/12 rad = 15 °

arccotangent of 2 + sqrt3 = pi/12 radians = 15 degrees

The arccot of 2 + sqrt3 is pi/12 radians, and the value in degrees is 15°. To change the result from the unit radian to the unit degree multiply the angle by 180° / $\pi$ and obtain 15°.

Our results above contain fractions of pi for the results in radian, and are exact values otherwise. If you compute arccot(2 + sqrt3), 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 + sqrt3 as decimal in the field labelled “x”. However, if you want to be given the angle of cot 2 + sqrt3 in radians, then you must press the swap units button.

### Calculate arccot x

The identities of arccotangent 2 + sqrt3 are as follows: arccot(2 + sqrt3) =

- $\frac{\pi}{2}$ – arctan(2 + sqrt3) ⇔ 90°- arctan(2 + sqrt3)
- $\pi$ – arccot(-2 + sqrt3) ⇔ 180°- arcot(-2 + sqrt3)
- arctan(1/2 + sqrt3)

The infinite series of arccot 2 + sqrt3 is: $\frac{\pi}{2}$ – $\sum_{n=0}^{\infty} \frac{(-1)^{n}(2+\sqrt{3})^{2n+1}}{(2n+1)}$.

Next, we discuss the derivative of arccot 2 + sqrt3 for x = 2 + sqrt3. In the following paragraph you can additionally learn what the search calculations form in the sidebar is used for.

## Derivative of arccot 2 + sqrt3

The derivative of arccot 2 + sqrt3 is particularly useful to calculate the inverse cotangent 2 + sqrt3 as an integral.

The formula for x is (arccot x)’ = – $\frac{1}{1 + x^{2}}$, x ≠ -1,1, so for x = 2 + sqrt3 the derivative equals -0.0669872981.

Using the arccot 2 + sqrt3 derivative, we can calculate the angle as a definite integral:

arccot 2 + sqrt3 = $\frac{\pi}{2}$ – $\int_{2+\sqrt{3}}^{\infty}\frac{1}{{1+z^{2}}}dz$.

The relationship of arccot of 2 + sqrt3 and the trigonometric functions sin, cos and tan is:

- sin(arccotangent(2 + sqrt3)) = $\frac{1}{\sqrt{1 + (2+\sqrt{3})^{2}}}$
- cos(arccotangent(2 + sqrt3)) = $\frac{2+\sqrt{3}}{\sqrt{1 + (2+\sqrt{3})^{2}}}$
- tan(arccotangent(2 + sqrt3)) = 1/2 + sqrt3

Note that you can locate many terms including the arccotangent(2 + sqrt3) value using the search form. On mobile devices you can find it by scrolling down. Enter, for instance, arccot2 + sqrt3 angle.

Using the aforementioned form in the same way, you can also look up terms including derivative of inverse cotangent 2 + sqrt3, inverse cotangent 2 + sqrt3, and derivative of arccot 2 + sqrt3, just to name a few.

In the next part of this article we discuss the trigonometric significance of arccotangent 2 + sqrt3, and there we also explain the difference between the inverse and the reciprocal of cot 2 + sqrt3.

## What is arccot 2 + sqrt3?

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 cot α = x / y = 2 + sqrt3. The angle whose cotangent value equals 2 + sqrt3 is α.

In the interval ]0, pi[ or ]0°, 180°[, there is only one α whose arccotangent value equals 2 + sqrt3. For that interval we define the function which determines the value of α as

From the definition of arccot(2 + sqrt3) follows that the *inverse* function y^{-1} = cot(y) = 2 + sqrt3. Observe that the *reciprocal* function of cot(y),(cot(y))^{-1} is 1/cot(y).

Avoid misconceptions and remember (cot(y))^{-1} = 1/cot(y) ≠ cot^{-1}(y) = arccot(2 + sqrt3). And make sure to understand that the trigonometric function y=arccot(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 = arccot(x) if and only if cot y = x and 0 < y < pi. The domain of x is $\mathbb{R}$.

## Conclusion

The frequently asked questions in the context include *what is arccot 2 + sqrt3 degrees* and *what is the inverse cotangent 2 + sqrt3* for example; reading our content they are no-brainers.

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– Article written by Mark