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Arcctg 10

Welcome to arcctg 10, our post aboutthe arccotangent of 10.

For the inverse trigonometric function of cotangent 10 we usually employ the abbreviation arcctg and write it as arcctg 10 or arcctg(10).

If you have been looking for what is arcctg 10, either in degrees or radians, or if you have been wondering about the inverse of ctg 10, then you are right here, too.

In this post you can find the angle arccotangent of 10, along with identities.

Read on to learn all about the arcctg of 10.

Arcctg of 10

If you want to know what is arcctg 10 in terms of trigonometry, check out the explanations in the last paragraph; ahead in this section is the value of arccotangent(10):

arcctg 10 = 0.1 rad = 5.711°
arccotangent 10 = 0.1 rad = 5.711 °
arccotangent of 10 = 0.1 radians = 5.711 degrees

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The arcctg of 10 is 0.1 radians, and the value in degrees is 5.711°. To change the result from the unit radian to the unit degree multiply the angle by 180° / $\pi$ and obtain 5.711°.

Our results above have been rounded to three decimal places. If you compute arcctg(10), 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 10 as decimal in the field labelled “x”. However, if you want to be given the angle of ctg 10 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 10, similar trigonometric calculations include:

The identities of arccotangent 10 are as follows: arcctg(10) =

  • $\frac{\pi}{2}$ – arctg(10) ⇔ 90°- arctg(10)
  • $\pi$ – arcctg(-10) ⇔ 180°- arctg(-10)
  • arctg(1/10)

The infinite series of arcctg 10 is: $\frac{\pi}{2}$ – $\sum_{n=0}^{\infty} \frac{(-1)^{n}(10)^{2n+1}}{(2n+1)}$.

Next, we discuss the derivative of arcctg 10 for x = 10. In the following paragraph you can additionally learn what the search calculations form in the sidebar is used for.

Derivative of arcctg 10

The derivative of arcctg 10 is particularly useful to calculate the inverse cotangent 10 as an integral.

The formula for x is (arcctg x)’ = – $\frac{1}{1 + x^{2}}$, x ≠ -1,1, so for x = 10 the derivative equals -0.0099009901.

Using the arcctg 10 derivative, we can calculate the angle as a definite integral:

arcctg 10 = $\frac{\pi}{2}$ – $\int_{10}^{\infty}\frac{1}{{1+z^{2}}}dz$.

The relationship of arcctg of 10 and the trigonometric functions sin, cos and tg is:

  • sin(arccotangent(10)) = $\frac{1}{\sqrt{1 + (10)^{2}}}$
  • cos(arccotangent(10)) = $\frac{10}{\sqrt{1 + (10)^{2}}}$
  • tg(arccotangent(10)) = 1/10

Note that you can locate many terms including the arccotangent(10) value using the search form. On mobile devices you can find it by scrolling down. Enter, for instance, arcctg10 angle.

Using the aforementioned form in the same way, you can also look up terms including derivative of inverse cotangent 10, inverse cotangent 10, and derivative of arcctg 10, just to name a few.

In the next part of this article we discuss the trigonometric significance of arccotangent 10, and there we also explain the difference between the inverse and the reciprocal of ctg 10.

What is arcctg 10?

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 = 10. The angle whose cotangent value equals 10 is α.

In the interval ]0, pi[ or ]0°, 180°[, there is only one α whose arccotangent value equals 10. For that interval we define the function which determines the value of α as

y = arcctg(10).

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From the definition of arcctg(10) follows that the inverse function y-1 = ctg(y) = 10. 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(10). 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 < π. The domain of x is $\mathbb{R}$.

Conclusion

Arcctg 10The frequently asked questions in the context include what is arcctg 10 degrees and what is the inverse cotangent 10 for example; reading our content they are no-brainers.

But, if there is something else about the topic you would like to know, fill in the form on the bottom of this post, or send us an email with a subject line such as arccotangent 10 in radians.

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– Article written by Mark, last updated on February 6th, 2017

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