Table of Contents
Welcome to arctan 0.6, our post aboutthe arctangent of 0.6.
For the inverse trigonometric function of tangent 0.6 we usually employ the abbreviation arctan and write it as arctan 0.6 or arctan(0.6).
If you have been looking for what is arctan 0.6, either in degrees or radians, or if you have been wondering about the inverse of tan 0.6, then you are right here, too.
In this post you can find the angle arctangent of 0.6, along with identities.
Read on to learn all about the arctan of 0.6.
Arctan of 0.6
If you want to know what is arctan 0.6 in terms of trigonometry, check out the explanations in the last paragraph; ahead in this section is the value of arctangent(0.6):
arctangent 0.6 = 0.54 rad = 30.964 °
arctangent of 0.6 = 0.54 radians = 30.964 degrees
The arctan of 0.6 is 0.54 radians, and the value in degrees is 30.964°. To change the result from the unit radian to the unit degree multiply the angle by 180° / $\pi$ and obtain 30.964°.
Our results above have been rounded to three decimal places. If you compute arctan(0.6), 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 0.6 as decimal in the field labelled “x”. However, if you want to be given the angle of tan 0.6 in radians, then you must press the swap units button.
Calculate arctan x
The identities of arctangent 0.6 are as follows: arctan(0.6) =
- $\frac{\pi}{2}$ – arccot(0.6) ⇔ 90°- arccot(0.6)
- -arctan(-0.6)
- arccot(1/0.6)
- $arcsin(\frac{0.6}{\sqrt{(0.6)^{2}+1}})$
- $2arctan(\frac{0.6}{1+\sqrt{(0.6)^{2}+1}})$
The infinite series of arctan 0.6 is: $\sum_{n=0}^{\infty} \frac{(-1)^{n}(0.6)^{2n+1}}{(2n+1)}$.
Next, we discuss the derivative of arctan 0.6 for x = 0.6. In the following paragraph you can additionally learn what the search calculations form in the sidebar is used for.
Derivative of arctan 0.6
The derivative of arctan 0.6 is particularly useful to calculate the inverse tangent 0.6 as an integral.
The formula for x is (arctan x)’ = $\frac{1}{1 + x^{2}}$, x ≠ -1,1, so for x = 0.6 the derivative equals 0.7352941176.
Using the arctan 0.6 derivative, we can calculate the angle as a definite integral:
arctan 0.6 = $\int_{0}^{0.6}\frac{1}{{1+z^{2}}}dz$.
The relationship of arctan of 0.6 and the trigonometric functions sin, cos and tan is:
- sin(arctangent(0.6)) = $\frac{0.6}{\sqrt{1 + (0.6)^{2}}}$
- cos(arctangent(0.6)) = $\frac{1}{\sqrt{1 + (0.6)^{2}}}$
- tan(arctangent(0.6)) = 0.6
Note that you can locate many terms including the arctangent(0.6) value using the search form. On mobile devices you can find it by scrolling down. Enter, for instance, arctan0.6 angle.
Using the aforementioned form in the same way, you can also look up terms including derivative of inverse tangent 0.6, inverse tangent 0.6, and derivative of arctan 0.6, just to name a few.
In the next part of this article we discuss the trigonometric significance of arctangent 0.6, and there we also explain the difference between the inverse and the reciprocal of tan 0.6.
What is arctan 0.6?
In a triangle which has one angle of 90 degrees, the sine of the angle α is the ratio of the length of the opposite side o to the length of the hypotenuse h: sin α = o/h, and 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, sin α = y / r = y, cos α = x / r = x, and tan α = y / x = 0.6. The angle whose tangent value equals 0.6 is α.
In the interval ]-π/2, π/2[ or ]-90°, 90°[, there is only one α whose arctangent value equals 0.6. For that interval we define the function which determines the value of α as
From the definition of arctan(0.6) follows that the inverse function y-1 = tan(y) = 0.6. Observe that the reciprocal function of tan(y),(tan(y))-1 is 1/tan(y).
Avoid misconceptions and remember (tan(y))-1 = 1/tan(y) ≠ tan-1(y) = arctan(0.6). And make sure to understand that the trigonometric function y=arctan(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 = arctan(x) if and only if tan y = x and -π/2 < y < π/2. The domain of x is $\mathbb{R}$.
Conclusion
The frequently asked questions in the context include what is arctan 0.6 degrees and what is the inverse tangent 0.6 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 arctangent 0.6 in radians.
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– Article written by Mark, last updated on February 5th, 2017