Table of Contents
Welcome to arccot sqrt3, our post aboutthe arccotangent of sqrt3.
For the inverse trigonometric function of cotangent sqrt3 we usually employ the abbreviation arccot and write it as arccot sqrt3 or arccot(sqrt3).
If you have been looking for what is arccot sqrt3, either in degrees or radians, or if you have been wondering about the inverse of cot sqrt3, then you are right here, too.
In this post you can find the angle arccotangent of sqrt3, along with identities.
Read on to learn all about the arccot of sqrt3, and note that the term sqrt3 is approximately 1.732050807 as a decimal number.
Arccot of sqrt3
If you want to know what is arccot sqrt3 in terms of trigonometry, check out the explanations in the last paragraph; ahead in this section is the value of arccotangent(sqrt3):
arccotangent sqrt3 = pi/6 rad = 30 °
arccotangent of sqrt3 = pi/6 radians = 30 degrees
The arccot of sqrt3 is pi/6 radians, and the value in degrees is 30°. To change the result from the unit radian to the unit degree multiply the angle by 180° / $\pi$ and obtain 30°.
Our results above contain fractions of pi for the results in radian, and are exact values otherwise. If you compute arccot(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 sqrt3 as decimal in the field labelled “x”. However, if you want to be given the angle of cot sqrt3 in radians, then you must press the swap units button.
Calculate arccot x
The identities of arccotangent sqrt3 are as follows: arccot(sqrt3) =
- $\frac{\pi}{2}$ – arctan(sqrt3) ⇔ 90°- arctan(sqrt3)
- $\pi$ – arccot(-sqrt3) ⇔ 180°- arcot(-sqrt3)
- arctan(1/sqrt3)
The infinite series of arccot sqrt3 is: $\frac{\pi}{2}$ – $\sum_{n=0}^{\infty} \frac{(-1)^{n}(\sqrt{3})^{2n+1}}{(2n+1)}$.
Next, we discuss the derivative of arccot sqrt3 for x = sqrt3. In the following paragraph you can additionally learn what the search calculations form in the sidebar is used for.
Derivative of arccot sqrt3
The derivative of arccot sqrt3 is particularly useful to calculate the inverse cotangent sqrt3 as an integral.
The formula for x is (arccot x)’ = – $\frac{1}{1 + x^{2}}$, x ≠ -1,1, so for x = sqrt3 the derivative equals -0.25.
Using the arccot sqrt3 derivative, we can calculate the angle as a definite integral:
arccot sqrt3 = $\frac{\pi}{2}$ – $\int_{\sqrt{3}}^{\infty}\frac{1}{{1+z^{2}}}dz$.
The relationship of arccot of sqrt3 and the trigonometric functions sin, cos and tan is:
- sin(arccotangent(sqrt3)) = $\frac{1}{\sqrt{1 + (\sqrt{3})^{2}}}$
- cos(arccotangent(sqrt3)) = $\frac{\sqrt{3}}{\sqrt{1 + (\sqrt{3})^{2}}}$
- tan(arccotangent(sqrt3)) = 1/sqrt3
Note that you can locate many terms including the arccotangent(sqrt3) value using the search form. On mobile devices you can find it by scrolling down. Enter, for instance, arccotsqrt3 angle.
Using the aforementioned form in the same way, you can also look up terms including derivative of inverse cotangent sqrt3, inverse cotangent sqrt3, and derivative of arccot sqrt3, just to name a few.
In the next part of this article we discuss the trigonometric significance of arccotangent sqrt3, and there we also explain the difference between the inverse and the reciprocal of cot sqrt3.
What is arccot 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 = sqrt3. The angle whose cotangent value equals sqrt3 is α.
In the interval ]0, pi[ or ]0°, 180°[, there is only one α whose arccotangent value equals sqrt3. For that interval we define the function which determines the value of α as
From the definition of arccot(sqrt3) follows that the inverse function y-1 = cot(y) = 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(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 sqrt3 degrees and what is the inverse cotangent sqrt3 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 sqrt3 in radians.
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– Article written by Mark, last updated on February 5th, 2017