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Welcome to cot 30°, our post aboutthe cotangent of 30 degrees.
For the cotangent of 30 degrees we use the abbreviation cot for the trigonometric function together with the degree symbol °, and write it as cot 30°.
If you have been looking for what is cot 30°, or if you have been wondering about cot 30 degrees in radians, then you are right here, too.
In this post you can find the cot 30° value, along with identities.
Read on to learn all about the cot of 30°.
Cot 30 Degrees
If you want to know what is cot 30 degrees in terms of trigonometry, then navigate straight to the explanations in the next paragraph; what’s ahead in this section is the value of cot 30°:
cot 30° = √3
cot 30 degrees = √3
The cot of 30 degrees is √3, the same as cot of 30 degrees in radians. To obtain 30 degrees in radian multiply 30° by $\pi$ / 180° = 1/6 $\pi$. Cot 30degrees = cot (1/6 × $\pi)$.
Our results of cot30° have been rounded to five decimal places. If you want cotangent 30° with higher accuracy, then use the calculator below; our tool displays ten decimal places.
To calculate cot 30 degrees insert the angle 30 in the field labelled °, but if you want to calculate cot 30 in radians, then you have to press the swap unit button first.
Calculate cot [degrees]
The identities of cotangent 30° are as follows:
= tan (90°-30°) = tan 60°
-cot30°
= cot (-30°) = -cot 30°
= tan (90°+30°) = tan 120°
= cot (180°-30°) = cot 150°
There are more formulas for the double angle (2 × 30°), half angle ((30/2)°) as well as the sum, difference and products of two angles such as 30° and β.
You can locate all of them in the respective article found in the header menu. To find everything about cot -30° click the link. And here is all about tan 30°, including, for instance, a converter.
In terms of the other five trigonometric functions, cot of 30° =
- $\pm\frac{\sqrt{1 – \sin^{2} 30^\circ}}{\sin 30^\circ}$
- $\pm\frac{\cos 30^\circ}{\sqrt{1 – \cos^{2} 30^\circ}}$
- $\pm \sqrt{\csc^{2} 30^\circ -1}$
- $\pm\frac{1}{\sqrt{\csc^2 30^\circ – 1}}$
- $\frac{1}{\tan 30^\circ}$
As the tangent function is the reciprocal of the cotangent function, 1 / tan 30° = cot30°.
In the next part of this article we discuss the trigonometric significance of cot30°, and there you can also learn what the search calculations form in the sidebar is used for.
What is cot 30°?
In a triangle which has one angle of 90 degrees, the cotangent of the angle of 30° is the ratio of the length of the adjacent side a to the length of the opposite side o: cot 30° = a/o.
In a circle with the radius r, the horizontal axis x, and the vertical axis y, 30 degrees is the angle formed by the two sides x and r; r moving counterclockwise is the positive angle.
Applying the unit-circle definition found on our homepage, assumed r = 1, in the intersection of the point (x,y) and the circle, y = sin 30°, x = cos 30° and cot 30° = cos 30°/sin 30°.
Bringing together the triangle definition and the unit circle definition of cotangent 30 degrees, a = x, o = y and h = r = 1. It follows that $x/y\hspace{5px} =\hspace{5px}\frac{adjacent}{opposite}\hspace{5px}=\hspace{5px}\cot 30^\circ$.
Note that you can locate many terms including the cotangent30° value using the search form. On mobile devices you can find it by scrolling down. Enter, for instance, value of cot30°.
Along the same lines, using the aforementioned form, can you look up terms such as cot 30° value, cot 30, cot30° value and what is the cot of 30 degrees, just to name a few.
Given the periodicity of cotangent of 30°, to determine the cotangent of an angle > 180°, e.g. 750°, calculate cot 750° as cot (750 Mod 180)° = cotangent of 30°, or use our form.
Conclusion
The frequently asked questions in the context include what is cot 30 degrees and what is the cot of 30 degrees for example; reading our content they are no-brainers.
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– Article written by Mark, last updated on February 26th, 2017