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Welcome to **arcsec 2√(3)/3**, our post aboutthe arcsecant of 2√(3)/3.

For the inverse trigonometric function of secant 2√(3)/3 we usually employ the abbreviation *arcsec* and write it as arcsec 2√(3)/3 or arcsec(2√(3)/3).

If you have been looking for *what is arcsec 2√(3)/3*, either in degrees or radians, or if you have been wondering about the inverse of sec 2√(3)/3, then you are right here, too.

In this post you can find the angle arcsecant of 2√(3)/3, along with identities.

Read on to learn all about the arcsec of 2√(3)/3, and note that the term 2√(3)/3 is approximately 1.154700538 as a decimal number.

## Arcsec of 2√(3)/3

If you want to know *what is arcsec 2√(3)/3* in terms of trigonometry, check out the explanations in the last paragraph; ahead in this section is the value of arcsecant(2√(3)/3):

arcsecant 2√(3)/3 = π/6 rad = 30 °

arcsecant of 2√(3)/3 = π/6 radians = 30 degrees

The arcsec of 2√(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 arcsec(2√(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 2√(3)/3 as decimal in the field labelled “x”. However, if you want to be given the angle of sec 2√(3)/3 in radians, then you must press the swap units button.

### Calculate arcsec x

The identities of arcsecant 2√(3)/3 are as follows: arcsec(2√(3)/3) =

- $\frac{\pi}{2}$ – arccsc(2√(3)/3) ⇔ 90°- arccsc(2√(3)/3)
- $\pi$ – arcsec(-2√(3)/3) ⇔ 180° – arcsec(-2√(3)/3)
- arccos($\frac{1}{2\frac{\sqrt{3}}{3}}$)

The infinite series of arcsec 2√(3)/3 is: $\frac{\pi}{2} – \sum_{n=0}^{\infty}\frac{\binom{2n}{n}(2\frac{\sqrt{3}}{3})^{-(2n+1)}}{4^{n}(2n+1)}$.

Next, we discuss the derivative of arcsec 2√(3)/3 for 2√(3)/3 = 2√(3)/3. In the following paragraph you can additionally learn what the search calculations form in the sidebar is used for.

## Derivative of arcsec 2√(3)/3

The derivative of arcsec 2√(3)/3 is particularly useful to calculate the inverse secant 2√(3)/3 as an integral.

The formula for x is (arcsec x)’ = $\frac{1}{|x|\sqrt{x^{2}-1}}$, |x| > 1, so for x = 2√(3)/3 the derivative equals 1.5.

Using the arcsec 2√(3)/3 derivative, we can calculate the angle as a definite integral:

arcsec 2√(3)/3 = $\int_{1}^{2\frac{\sqrt{3}}{3}}\frac{1}{z\sqrt{z^{2}-1}}dz$.

The relationship of arcsec of 2√(3)/3 and the trigonometric functions sin, cos and tan is:

- sin(arcsecant(2√(3)/3)) = $\frac{\sqrt{(2\frac{\sqrt{3}}{3})^{2}-1}}{2\frac{\sqrt{3}}{3}}$
- cos(arcsecant(2√(3)/3)) = $\frac{1}{2\frac{\sqrt{3}}{3}}$
- tan(arcsecant(2√(3)/3)) = $\sqrt{(2\frac{\sqrt{3}}{3})^{2}-1}$

Note that you can locate many terms including the arcsecant(2√(3)/3) value using the search form. On mobile devices you can find it by scrolling down. Enter, for instance, arcsec2√(3)/3 angle.

Using the aforementioned form in the same way, you can also look up terms including derivative of inverse secant 2√(3)/3, inverse secant 2√(3)/3, and derivative of arcsec 2√(3)/3, just to name a few.

In the next part of this article we discuss the trigonometric significance of arcsecant 2√(3)/3, and there we also explain the difference between the inverse and the reciprocal of sec 2√(3)/3.

## What is arcsec 2√(3)/3?

In a triangle which has one angle of 90 degrees, 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, cos α = x / r = x, and sec α = 1 / x = 2√(3)/3. The angle whose secant value equals 2√(3)/3 is α.

In the interval [0, π/2[ ∪ ]π/2, π] or [0°, 90°[ ∪ ]90°, 180°], there is only one α whose secant value equals 2√(3)/3. For that interval we define the function which determines the value of α as

From the definition of arcsec(2√(3)/3) follows that the *inverse* function y^{-1} = sec(y) = 2√(3)/3. Observe that the *reciprocal* function of sec(y),(sec(y))^{-1} is 1/sec(y) = cos(y).

Avoid misconceptions and remember (sec(y))^{-1} = 1/sec(y) ≠ sec^{-1}(y) = arcsec(2√(3)/3). And make sure to understand that the trigonometric function y=arcsec(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 = arcsec(x) if and only if sec y = x and 0 ≤ y < π/2 or sec y = x and π/2 < y ≤ π. The domain of x is x ≤ −1 or 1 ≤ x.

## Conclusion

The frequently asked questions in the context include *what is arcsec 2√(3)/3 degrees* and *what is the inverse secant 2√(3)/3* for example; reading our content they are no-brainers.

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