Table of Contents
Welcome to tan 18°, our post aboutthe tangent of 18 degrees.
For the tangent of 18 degrees we use the abbreviation tan for the trigonometric function together with the degree symbol °, and write it as tan 18°.
If you have been looking for what is tan 18°, or if you have been wondering about tan 18 degrees in radians, then you are right here, too.
In this post you can find the tan 18° value, along with identities.
Read on to learn all about the tan of 18°.
Tan 18 Degrees
If you want to know what is tan 18 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 tan 18°:
tan 18° = 0.32492
tan 18 degrees = 0.32492
The tan of 18 degrees is 0.32492, the same as tan of 18 degrees in radians. To obtain 18 degrees in radian multiply 18° by $\pi$ / 180° = 1/10 $\pi$. Tan 18degrees = tan (1/10 × $\pi)$.
Our results of tan18° have been rounded to five decimal places. If you want tangent 18° with higher accuracy, then use the calculator below; our tool displays ten decimal places.
To calculate tan 18 degrees insert the angle 18 in the field labelled °, but if you want to calculate tan 18 in radians, then you have to press the swap unit button first.
Calculate tan [degrees]
The identities of tangent 18° are as follows:
= cot (90°-18°) = cot 72°
-tan18°
= tan (-18°) = -tan 18°
= cot (90°+18°) = cot 108°
= tan (180°-18°) = tan 162°
There are more formulas for the double angle (2 × 18°), half angle ((18/2)°) as well as the sum, difference and products of two angles such as 18° and β.
You can locate all of them in the respective article found in the header menu. To find everything about tan -18° click the link. And here is all about cot 18°, including, for instance, a converter.
In terms of the other five trigonometric functions, tan of 18° =
- $\pm\frac{\sin 18^\circ}{\sqrt{1 – \sin^{2} 18^\circ}}$
- $\pm\frac{\sqrt{1 – \cos^{2} 18^\circ}}{\cos 18^\circ}$
- $\pm \sqrt{\sec^{2} 18^\circ -1}$
- $\pm\frac{1}{\sqrt{\csc^2 18^\circ – 1}}$
- $\frac{1}{\cot 18^\circ}$
As the cotangent function is the reciprocal of the tangent function, 1 / cot 18° = tan18°.
In the next part of this article we discuss the trigonometric significance of tan18°, and there you can also learn what the search calculations form in the sidebar is used for.
What is tan 18°?
In a triangle which has one angle of 90 degrees, the tangent of the angle of 18° is the ratio of the length of the opposite side o to the length of the adjacent side a: tan 18° = o/a.
In a circle with the radius r, the horizontal axis x, and the vertical axis y, 18 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 18°, x = cos 18° and tan 18° = sin 18°/cos 18°.
Bringing together the triangle definition and the unit circle definition of tangent 18 degrees, a = x, o = y and h = r = 1. It follows that $y/x\hspace{5px} =\hspace{5px}\frac{opposite}{adjacent}\hspace{5px}=\hspace{5px}\tan 18^\circ$.
Note that you can locate many terms including the tangent18° value using the search form. On mobile devices you can find it by scrolling down. Enter, for instance, value of tan18°.
Along the same lines, using the aforementioned form, can you look up terms such as tan 18° value, tan 18, tan18° value and what is the tan of 18 degrees, just to name a few.
Given the periodicity of tangent of 18°, to determine the tangent of an angle > 180°, e.g. 738°, calculate tan 738° as tan (738 Mod 180)° = tangent of 18°, or look it up with our form.
Conclusion
The frequently asked questions in the context include what is tan 18 degrees and what is the tan of 18 degrees for example; reading our content they are no-brainers.
But, if there is something else about tangent 18° 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 tangent 18 degrees.
If our calculator and the information on tan18° 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 tan18 degrees.
– Article written by Mark, last updated on February 18th, 2017