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Welcome to tan 61°, our post aboutthe tangent of 61 degrees.
For the tangent of 61 degrees we use the abbreviation tan for the trigonometric function together with the degree symbol °, and write it as tan 61°.
If you have been looking for what is tan 61°, or if you have been wondering about tan 61 degrees in radians, then you are right here, too.
In this post you can find the tan 61° value, along with identities.
Read on to learn all about the tan of 61°.
Tan 61 Degrees
If you want to know what is tan 61 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 61°:
tan 61° = 1.80405
tan 61 degrees = 1.80405
The tan of 61 degrees is 1.80405, the same as tan of 61 degrees in radians. To obtain 61 degrees in radian multiply 61° by $\pi$ / 180° = 61/180 $\pi$. Tan 61degrees = tan (61/180 × $\pi)$.
Our results of tan61° have been rounded to five decimal places. If you want tangent 61° with higher accuracy, then use the calculator below; our tool displays ten decimal places.
To calculate tan 61 degrees insert the angle 61 in the field labelled °, but if you want to calculate tan 61 in radians, then you have to press the swap unit button first.
Calculate tan [degrees]
The identities of tangent 61° are as follows:
= cot (90°-61°) = cot 29°
-tan61°
= tan (-61°) = -tan 61°
= cot (90°+61°) = cot 151°
= tan (180°-61°) = tan 119°
There are more formulas for the double angle (2 × 61°), half angle ((61/2)°) as well as the sum, difference and products of two angles such as 61° and β.
You can locate all of them in the respective article found in the header menu. To find everything about tan -61° click the link. And here is all about cot 61°, including, for instance, a converter.
In terms of the other five trigonometric functions, tan of 61° =
- $\pm\frac{\sin 61^\circ}{\sqrt{1 – \sin^{2} 61^\circ}}$
- $\pm\frac{\sqrt{1 – \cos^{2} 61^\circ}}{\cos 61^\circ}$
- $\pm \sqrt{\sec^{2} 61^\circ -1}$
- $\pm\frac{1}{\sqrt{\csc^2 61^\circ – 1}}$
- $\frac{1}{\cot 61^\circ}$
As the cotangent function is the reciprocal of the tangent function, 1 / cot 61° = tan61°.
In the next part of this article we discuss the trigonometric significance of tan61°, and there you can also learn what the search calculations form in the sidebar is used for.
What is tan 61°?
In a triangle which has one angle of 90 degrees, the tangent of the angle of 61° is the ratio of the length of the opposite side o to the length of the adjacent side a: tan 61° = o/a.
In a circle with the radius r, the horizontal axis x, and the vertical axis y, 61 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 61°, x = cos 61° and tan 61° = sin 61°/cos 61°.
Bringing together the triangle definition and the unit circle definition of tangent 61 degrees, a = x, o = y and h = r = 1. It follows that $y/x\hspace{5px} =\hspace{5px}\frac{opposite}{adjacent}\hspace{5px}=\hspace{5px}\tan 61^\circ$.
Note that you can locate many terms including the tangent61° value using the search form. On mobile devices you can find it by scrolling down. Enter, for instance, value of tan61°.
Along the same lines, using the aforementioned form, can you look up terms such as tan 61° value, tan 61, tan61° value and what is the tan of 61 degrees, just to name a few.
Given the periodicity of tangent of 61°, to determine the tangent of an angle > 180°, e.g. 781°, calculate tan 781° as tan (781 Mod 180)° = tangent of 61°, or look it up with our form.
Conclusion
The frequently asked questions in the context include what is tan 61 degrees and what is the tan of 61 degrees for example; reading our content they are no-brainers.
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– Article written by Mark, last updated on February 18th, 2017