For the inverse trigonometric function of cosine sqrt(3)/2 we usually employ the abbreviation *arccos* and write it as arccos sqrt(3)/2 or arccos(sqrt(3)/2).

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

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

Read on to learn all about the arccos of sqrt(3)/2, and note that the term sqrt(3)/2 is approximately 0.866025403 as a decimal number.

## Arccos of sqrt(3)/2

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

arccos sqrt(3)/2 = pi/6 rad = 30°arccosine sqrt(3)/2 = pi/6 rad = 30 °arccosine of sqrt(3)/2 = pi/6 radians = 30 degrees” onclick=”if (!window.__cfRLUnblockHandlers) return false; return fbs_click()” target=”_blank” rel=”nofollow noopener noreferrer” data-cf-modified-1f43335a1d283acf098601e5-=””>

The arccos of sqrt(3)/2 is pi/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 pi for the results in radian, and are exact values otherwise. If you compute arccos(sqrt(3)/2), 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)/2 as decimal in the field labelled “x”. However, if you want to be given the angle adjacent to sqrt(3)/2 in radians, then you must press the swap units button.

### Calculate arccos x

x:

A Really Cool Arccosine Calculator and Useful Information! Please ReTweet. Click To TweetApart from the inverse of cos sqrt(3)/2, similar trigonometric calculations include:

The identities of arccosine sqrt(3)/2 are as follows: arccos(sqrt(3)/2) =

$frac{pi}{2}$ – arcsin(sqrt(3)/2) ⇔ 90°- arcsin(sqrt(3)/2) ${pi}$ – arccos(-sqrt(3)/2) ⇔ 180° – arcos(-sqrt(3)/2) arcsec(1/sqrt(3)/2) $arcsin(sqrt{1-(frac{sqrt{3}}{2})^{2}})$ $2arctan(frac{sqrt{1-(frac{sqrt{3}}{2})^{2}}}{1+(frac{sqrt{3}}{2})})$

The infinite series of arccos sqrt(3)/2 is: $frac{pi}{2}$ – $sum_{n=0}^{infty} frac{(2n)!}{2^{2n}(n!)^{2}(2n+1)}(frac{sqrt{3}}{2})^{2n+1}$.

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

## Derivative of arccos sqrt(3)/2

The derivative of arccos sqrt(3)/2 is particularly useful to calculate the inverse cosine sqrt(3)/2 as an integral.

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

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

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

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

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

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

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

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

## What is arccos sqrt(3)/2?

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, x = cos α = sqrt(3)/2 / r = sqrt(3)/2. The angle whose cosine value equals sqrt(3)/2 is α.

In the interval <0, pi> or <0°, 180°>, there is only one α whose arccosine value equals sqrt(3)/2. For that interval we define the function which determines the value of α as y = arccos(sqrt(3)/2).” onclick=”if (!window.__cfRLUnblockHandlers) return false; return fbs_click()” target=”_blank” rel=”nofollow noopener noreferrer” data-cf-modified-1f43335a1d283acf098601e5-=””>

From the definition of arccos(sqrt(3)/2) follows that the *inverse* function y-1 = cos(y) = sqrt(3)/2. Observe that the *reciprocal* function of cos(y),(cos(y))-1 is 1/cos(y).

Avoid misconceptions and remember (cos(y))-1 = 1/cos(y) ≠ cos-1(y) = arccos(sqrt(3)/2). And make sure to understand that the trigonometric function y=arccos(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 = arccos(x) if and only if cos y = x and 0 ≤ y ≤ pi. The domain of x is −1 ≤ x ≤ 1.

## Conclusion

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

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