Table of Contents

Welcome to **arcsec sqrt2 – sqrt6**, our post aboutthe arcsecant of sqrt2 – sqrt6.

For the inverse trigonometric function of secant sqrt2 – sqrt6 we usually employ the abbreviation *arcsec* and write it as arcsec sqrt2 – sqrt6 or arcsec(sqrt2 – sqrt6).

If you have been looking for *what is arcsec sqrt2 – sqrt6*, either in degrees or radians, or if you have been wondering about the inverse of sec sqrt2 – sqrt6, then you are right here, too.

In this post you can find the angle arcsecant of sqrt2 – sqrt6, along with identities.

Read on to learn all about the arcsec of sqrt2 – sqrt6, and note that the term sqrt2-sqrt6 is approximately -1.03527618 as a decimal number.

## Arcsec of sqrt2 – sqrt6

If you want to know *what is arcsec sqrt2 – sqrt6* in terms of trigonometry, check out the explanations in the last paragraph; ahead in this section is the value of arcsecant(sqrt2 – sqrt6):

arcsecant sqrt2 – sqrt6 = 11pi/12 rad = 165 °

arcsecant of sqrt2 – sqrt6 = 11pi/12 radians = 165 degrees

The arcsec of sqrt2 – sqrt6 is 11pi/12 radians, and the value in degrees is 165°. To change the result from the unit radian to the unit degree multiply the angle by 180° / $\pi$ and obtain 165°.

Our results above contain fractions of pi for the results in radian, and are exact values otherwise. If you compute arcsec(sqrt2 – sqrt6), 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 sqrt2 – sqrt6 as decimal in the field labelled “x”. However, if you want to be given the angle of sec sqrt2 – sqrt6 in radians, then you must press the swap units button.

### Calculate arcsec x

The identities of arcsecant sqrt2 – sqrt6 are as follows: arcsec(sqrt2 – sqrt6) =

- $\frac{\pi}{2}$ – arccsc(sqrt2 – sqrt6) ⇔ 90°- arccsc(sqrt2 – sqrt6)
- $\pi$ – arcsec(-sqrt2 – sqrt6) ⇔ 180° – arcsec(-sqrt2 – sqrt6)
- arccos($\frac{1}{\sqrt{2}-sqrt6}$)

The infinite series of arcsec sqrt2 – sqrt6 is: $\frac{\pi}{2} – \sum_{n=0}^{\infty}\frac{\binom{2n}{n}(\sqrt{2}-sqrt6)^{-(2n+1)}}{4^{n}(2n+1)}$.

Next, we discuss the derivative of arcsec sqrt2 – sqrt6 for sqrt2 – sqrt6 = sqrt2 – sqrt6. In the following paragraph you can additionally learn what the search calculations form in the sidebar is used for.

## Derivative of arcsec sqrt2 – sqrt6

The derivative of arcsec sqrt2 – sqrt6 is particularly useful to calculate the inverse secant sqrt2 – sqrt6 as an integral.

The formula for x is (arcsec x)’ = $\frac{1}{|x|\sqrt{x^{2}-1}}$, |x| > 1, so for x = sqrt2 – sqrt6 the derivative equals 3.6048842601.

Using the arcsec sqrt2 – sqrt6 derivative, we can calculate the angle as a definite integral:

arcsec sqrt2 – sqrt6 = $\int_{1}^{\sqrt{2}-sqrt6}\frac{1}{z\sqrt{z^{2}-1}}dz$.

The relationship of arcsec of sqrt2 – sqrt6 and the trigonometric functions sin, cos and tan is:

- sin(arcsecant(sqrt2 – sqrt6)) = $\frac{\sqrt{(\sqrt{2}-sqrt6)^{2}-1}}{\sqrt{2}-sqrt6}$
- cos(arcsecant(sqrt2 – sqrt6)) = $\frac{1}{\sqrt{2}-sqrt6}$
- tan(arcsecant(sqrt2 – sqrt6)) = $\sqrt{(\sqrt{2}-sqrt6)^{2}-1}$

Note that you can locate many terms including the arcsecant(sqrt2 – sqrt6) value using the search form. On mobile devices you can find it by scrolling down. Enter, for instance, arcsecsqrt2 – sqrt6 angle.

Using the aforementioned form in the same way, you can also look up terms including derivative of inverse secant sqrt2 – sqrt6, inverse secant sqrt2 – sqrt6, and derivative of arcsec sqrt2 – sqrt6, just to name a few.

In the next part of this article we discuss the trigonometric significance of arcsecant sqrt2 – sqrt6, and there we also explain the difference between the inverse and the reciprocal of sec sqrt2 – sqrt6.

## What is arcsec sqrt2 – sqrt6?

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 = sqrt2 – sqrt6. The angle whose secant value equals sqrt2 – sqrt6 is α.

In the interval [0, pi/2[ ∪ ]pi/2, pi] or [0°, 90°[ ∪ ]90°, 180°], there is only one α whose secant value equals sqrt2 – sqrt6. For that interval we define the function which determines the value of α as

From the definition of arcsec(sqrt2 – sqrt6) follows that the *inverse* function y^{-1} = sec(y) = sqrt2 – sqrt6. 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(sqrt2 – sqrt6). 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 < pi/2 or sec y = x and pi/2 < y ≤ pi. The domain of x is x ≤ −1 or 1 ≤ x.

## Conclusion

The frequently asked questions in the context include *what is arcsec sqrt2 – sqrt6 degrees* and *what is the inverse secant sqrt2 – sqrt6* for example; reading our content they are no-brainers.

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– Article written by Mark, last updated on February 4th, 2017