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# Arcsec -(sqrt6 + sqrt2)

Welcome to arcsec -(sqrt6 + sqrt2), our post aboutthe arcsecant of -(sqrt6 + sqrt2).

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

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

In this post you can find the angle arcsecant of -(sqrt6 + sqrt2), along with identities.

Read on to learn all about the arcsec of -(sqrt6 + sqrt2), and note that the term -sqrt6-sqrt2 is approximately -3.8637033 as a decimal number.

## Arcsec of -(sqrt6 + sqrt2)

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

arcsec -(sqrt6 + sqrt2) = 7pi/12 rad = 105°
arcsecant -(sqrt6 + sqrt2) = 7pi/12 rad = 105 °
arcsecant of -(sqrt6 + sqrt2) = 7pi/12 radians = 105 degrees

The arcsec of -(sqrt6 + sqrt2) is 7pi/12 radians, and the value in degrees is 105°. To change the result from the unit radian to the unit degree multiply the angle by 180° / $\pi$ and obtain 105°.

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

### Calculate arcsec x

Apart from the inverse of sec -(sqrt6 + sqrt2), similar trigonometric calculations include:

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

• $\frac{\pi}{2}$ – arccsc(-(sqrt6 + sqrt2)) ⇔ 90°- arccsc(-(sqrt6 + sqrt2))
• $\pi$ – arcsec((sqrt6 + sqrt2)) ⇔ 180° – arcsec((sqrt6 + sqrt2))
• arccos($\frac{1}{-(\sqrt{6}+\sqrt{2})}$)

The infinite series of arcsec -(sqrt6 + sqrt2) is: $\frac{\pi}{2} – \sum_{n=0}^{\infty}\frac{\binom{2n}{n}(-(\sqrt{6}+\sqrt{2}))^{-(2n+1)}}{4^{n}(2n+1)}$.

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

## Derivative of arcsec -(sqrt6 + sqrt2)

The derivative of arcsec -(sqrt6 + sqrt2) is particularly useful to calculate the inverse secant -(sqrt6 + sqrt2) as an integral.

The formula for x is (arcsec x)’ = $\frac{1}{|x|\sqrt{x^{2}-1}}$, |x| > 1, so for x = -(sqrt6 + sqrt2) the derivative equals 0.0693503541.

Using the arcsec -(sqrt6 + sqrt2) derivative, we can calculate the angle as a definite integral:

arcsec -(sqrt6 + sqrt2) = $\int_{1}^{-(\sqrt{6}+\sqrt{2})}\frac{1}{z\sqrt{z^{2}-1}}dz$.

The relationship of arcsec of -(sqrt6 + sqrt2) and the trigonometric functions sin, cos and tan is:

• sin(arcsecant(-(sqrt6 + sqrt2))) = $\frac{\sqrt{(-(\sqrt{6}+\sqrt{2}))^{2}-1}}{-(\sqrt{6}+\sqrt{2})}$
• cos(arcsecant(-(sqrt6 + sqrt2))) = $\frac{1}{-(\sqrt{6}+\sqrt{2})}$
• tan(arcsecant(-(sqrt6 + sqrt2))) = $\sqrt{(-(\sqrt{6}+\sqrt{2}))^{2}-1}$

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

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

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

## What is arcsec -(sqrt6 + sqrt2)?

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 = -(sqrt6 + sqrt2). The angle whose secant value equals -(sqrt6 + sqrt2) 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 -(sqrt6 + sqrt2). For that interval we define the function which determines the value of α as

y = arcsec(-(sqrt6 + sqrt2)).

From the definition of arcsec(-(sqrt6 + sqrt2)) follows that the inverse function y-1 = sec(y) = -(sqrt6 + sqrt2). 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(-(sqrt6 + sqrt2)). 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 -(sqrt6 + sqrt2) degrees and what is the inverse secant -(sqrt6 + sqrt2) for example; reading our content they are no-brainers.

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