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Arcctg -(2+sqrt3)

Welcome to arcctg -(2+sqrt3), our post aboutthe arccotangent of -(2+sqrt3).

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

If you have been looking for what is arcctg -(2+sqrt3), either in degrees or radians, or if you have been wondering about the inverse of ctg -(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 arcctg of -(2+sqrt3), and note that the term -2-sqrt3 is approximately -3.7320508 as a decimal number.

Arcctg of -(2+sqrt3)

If you want to know what is arcctg -(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)):

arcctg -(2+sqrt3) = 11pi/12 rad = 165°
arccotangent -(2+sqrt3) = 11pi/12 rad = 165 °
arccotangent of -(2+sqrt3) = 11pi/12 radians = 165 degrees

The arcctg of -(2+sqrt3) 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+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 ctg -(2+sqrt3) in radians, then you must press the swap units button.

Calculate arcctg x

Apart from the inverse of ctg -(2+sqrt3), similar trigonometric calculations include:

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

• $\frac{\pi}{2}$ – arctg(-(2+sqrt3)) ⇔ 90°- arctg(-(2+sqrt3))
• $\pi$ – arcctg((2+sqrt3)) ⇔ 180°- arctg((2+sqrt3))
• arctg(1/-(2+sqrt3)) + $\pi$

The infinite series of arcctg -(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 arcctg -(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 arcctg -(2+sqrt3)

The derivative of arcctg -(2+sqrt3) is particularly useful to calculate the inverse cotangent -(2+sqrt3) as an integral.

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

Using the arcctg -(2+sqrt3) derivative, we can calculate the angle as a definite integral:

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

The relationship of arcctg of -(2+sqrt3) and the trigonometric functions sin, cos and tg is:

• sin(arccotangent(-(2+sqrt3))) = $\frac{1}{\sqrt{1 + (-(2+\sqrt{3}))^{2}}}$
• cos(arccotangent(-(2+sqrt3))) = $\frac{-(2+\sqrt{3})}{\sqrt{1 + (-(2+\sqrt{3}))^{2}}}$
• tg(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, arcctg-(2+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 arcctg -(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 ctg -(2+sqrt3).

What is arcctg -(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 ctg 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

y = arcctg(-(2+sqrt3)).

From the definition of arcctg(-(2+sqrt3)) follows that the inverse function y-1 = ctg(y) = -(2+sqrt3). 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+sqrt3)). 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+sqrt3) degrees and what is the inverse cotangent -(2+sqrt3) for example; reading our content they are no-brainers.

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