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Arctg -sqrt(3)/3

Welcome to arctg -sqrt(3)/3, our post aboutthe arctangent of -sqrt(3)/3.

For the inverse trigonometric function of tangent -sqrt(3)/3 we usually employ the abbreviation arctg and write it as arctg -sqrt(3)/3 or arctg(-sqrt(3)/3).

If you have been looking for what is arctg -sqrt(3)/3, either in degrees or radians, or if you have been wondering about the inverse of tg -sqrt(3)/3, then you are right here, too.

In this post you can find the angle arctangent of -sqrt(3)/3, along with identities.

Read on to learn all about the arctg of -sqrt(3)/3, and note that the term -sqrt(3)/3 is approximately -0.57735026 as a decimal number.

Arctg of -sqrt(3)/3

If you want to know what is arctg -sqrt(3)/3 in terms of trigonometry, check out the explanations in the last paragraph; ahead in this section is the value of arctangent(-sqrt(3)/3):

arctg -sqrt(3)/3 = -π/6 rad = -30°
arctangent -sqrt(3)/3 = -π/6 rad = -30 °
arctangent of -sqrt(3)/3 = -π/6 radians = -30 degrees

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The arctg of -sqrt(3)/3 is -π/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 π for the results in radian, and are exact values otherwise. If you compute arctg(-sqrt(3)/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 -sqrt(3)/3 as decimal in the field labelled “x”. However, if you want to be given the angle of tg -sqrt(3)/3 in radians, then you must press the swap units button.

Calculate arctg x

A Really Cool Arctangent Calculator and Useful Information! Please ReTweet. Click To TweetApart from the inverse of tg -sqrt(3)/3, similar trigonometric calculations include:

The identities of arctangent -sqrt(3)/3 are as follows: arctg(-sqrt(3)/3) =

  • $\frac{\pi}{2}$ – arcctg(-sqrt(3)/3) ⇔ 90°- arcctg(-sqrt(3)/3)
  • -arctg(√(3)/3)
  • arcctg(1/-sqrt(3)/3) – $\pi $ ⇔ arcctg(1/-sqrt(3)/3) – 180°
  • $arcsin(\frac{-\frac{\sqrt{3}}{3}}{\sqrt{(-\frac{\sqrt{3}}{3})^{2}+1}})$
  • $2arctg(\frac{-\frac{\sqrt{3}}{3}}{1+\sqrt{(-\frac{\sqrt{3}}{3})^{2}+1}})$

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

Next, we discuss the derivative of arctg -sqrt(3)/3 for x = -sqrt(3)/3. In the following paragraph you can additionally learn what the search calculations form in the sidebar is used for.

Derivative of arctg -sqrt(3)/3

The derivative of arctg -sqrt(3)/3 is particularly useful to calculate the inverse tangent -sqrt(3)/3 as an integral.

The formula for x is (arctg x)’ = $\frac{1}{1 + x^{2}}$, x ≠ -1,1, so for x = -sqrt(3)/3 the derivative equals 0.75.

Using the arctg -sqrt(3)/3 derivative, we can calculate the angle as a definite integral:

arctg -sqrt(3)/3 = $\int_{0}^{-\frac{\sqrt{3}}{3}}\frac{1}{{1+z^{2}}}dz$.

The relationship of arctg of -sqrt(3)/3 and the trigonometric functions sin, cos and tg is:

  • sin(arctangent(-sqrt(3)/3)) = $\frac{-\frac{\sqrt{3}}{3}}{\sqrt{1 + (-\frac{\sqrt{3}}{3})^{2}}}$
  • cos(arctangent(-sqrt(3)/3)) = $\frac{1}{\sqrt{1 + (-\frac{\sqrt{3}}{3})^{2}}}$
  • tg(arctangent(-sqrt(3)/3)) = -sqrt(3)/3

Note that you can locate many terms including the arctangent(-sqrt(3)/3) value using the search form. On mobile devices you can find it by scrolling down. Enter, for instance, arctg-sqrt(3)/3 angle.

Using the aforementioned form in the same way, you can also look up terms including derivative of inverse tangent -sqrt(3)/3, inverse tangent -sqrt(3)/3, and derivative of arctg -sqrt(3)/3, just to name a few.

In the next part of this article we discuss the trigonometric significance of arctangent -sqrt(3)/3, and there we also explain the difference between the inverse and the reciprocal of tg -sqrt(3)/3.

What is arctg -sqrt(3)/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 tg α = y / x = -sqrt(3)/3. The angle whose tangent value equals -sqrt(3)/3 is α.

In the interval ]-π/2, π/2[ or ]-90°, 90°[, there is only one α whose arctangent value equals -sqrt(3)/3. For that interval we define the function which determines the value of α as

y = arctg(-sqrt(3)/3).

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From the definition of arctg(-sqrt(3)/3) follows that the inverse function y-1 = tg(y) = -sqrt(3)/3. Observe that the reciprocal function of tg(y),(tg(y))-1 is 1/tg(y).

Avoid misconceptions and remember (tg(y))-1 = 1/tg(y) ≠ tg-1(y) = arctg(-sqrt(3)/3). And make sure to understand that the trigonometric function y=arctg(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 = arctg(x) if and only if tg y = x and -π/2 < y < π/2. The domain of x is $\mathbb{R}$.

Conclusion

Arctg -sqrt(3)/3The frequently asked questions in the context include what is arctg -sqrt(3)/3 degrees and what is the inverse tangent -sqrt(3)/3 for example; reading our content they are no-brainers.

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

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