Skip to content
Home » Arcsecant » Arcsec -sqrt2

Arcsec -sqrt2

Welcome to arcsec -sqrt2, our post aboutthe arcsecant of -sqrt2.

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

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

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

Read on to learn all about the arcsec of -sqrt2, and note that the term -sqrt2 is approximately -1.41421356 as a decimal number.

Arcsec of -sqrt2

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

arcsec -sqrt2 = 3pi/4 rad = 135°
arcsecant -sqrt2 = 3pi/4 rad = 135 °
arcsecant of -sqrt2 = 3pi/4 radians = 135 degrees

Share on Facebook

The arcsec of -sqrt2 is 3pi/4 radians, and the value in degrees is 135°. To change the result from the unit radian to the unit degree multiply the angle by 180° / $\pi$ and obtain 135°.

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

Calculate arcsec x

A Really Cool Arcsecant Calculator and Useful Information! Please ReTweet. Click To TweetApart from the inverse of sec -sqrt2, similar trigonometric calculations include:

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

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

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

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

Derivative of arcsec -sqrt2

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

The formula for x is (arcsec x)’ = $\frac{1}{|x|\sqrt{x^{2}-1}}$, |x| > 1, so for x = -sqrt2 the derivative equals 0.7071067812.

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

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

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

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

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

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

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

What is arcsec -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 = -sqrt2. The angle whose secant value equals -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 -sqrt2. For that interval we define the function which determines the value of α as

y = arcsec(-sqrt2).

Share on Facebook

From the definition of arcsec(-sqrt2) follows that the inverse function y-1 = sec(y) = -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(-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.


Arcsec -sqrt2The frequently asked questions in the context include what is arcsec -sqrt2 degrees and what is the inverse secant -sqrt2 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 arcsecant -sqrt2 in radians.

If our calculator and the information on sec -sqrt2 inverse have been helpful, please hit the sharing buttons to spread the word about our content, and don’t forget to bookmark us.

Or, even better, install absolutely free PWA app (see menu or sidebar)!

Thanks for visiting our post.

Leave a Reply

Your email address will not be published. Required fields are marked *