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Arcctg -2+√3

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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 -0.26794919 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):

arcctg -2+√3 = 7pi/12 rad = 105°
arccotangent -2+√3 = 7pi/12 rad = 105 °
arccotangent of -2+√3 = 7pi/12 radians = 105 degrees

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The arcctg of -2+√3 is 7pi/12 radians, and the value in degrees is 105°. To change the result from the unit radian to the unit degree multiply the angle by 180° / $\pi$ and obtain 105°.

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

A Really Cool Arccotangent Calculator and Useful Information! Please ReTweet. Click To TweetApart from the inverse of ctg -2+√3, similar trigonometric calculations include:

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 -0.9330127019.

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

y = arcctg(-2+√3).

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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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