Table of Contents
Welcome to sec 80°, our post aboutthe secant of 80 degrees.
For the secant of 80 degrees we use the abbreviation sec for the trigonometric function together with the degree symbol °, and write it as sec 80°.
If you have been looking for what is sec 80°, or if you have been wondering about sec 80 degrees in radians, then you are right here, too.
In this post you can find the sec 80° value, along with identities.
Read on to learn all about the sec of 80°.
Sec 80 Degrees
If you want to know what is sec 80 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 sec 80°:
sec 80° = 5.75877
sec 80 degrees = 5.75877
The sec of 80 degrees is 5.75877, the same as sec of 80 degrees in radians. To obtain 80 degrees in radian multiply 80° by $\pi$ / 180° = 4/9 $\pi$. Sec 80degrees = sec (4/9 × $\pi)$.
Our results of sec80° have been rounded to five decimal places. If you want secant 80° with higher accuracy, then use the calculator below; our tool displays ten decimal places.
To calculate sec 80 degrees insert the angle 80 in the field labelled °, but if you want to calculate sec 80 in radians, then you have to press the swap unit button first.
Calculate sec [degrees]
Note that sec80° is periodic: sec (80° + n × 360°) = sec 80 degrees, n$\hspace{5px} \in \hspace{5px} \mathbb{Z}$.
In terms of the other five trigonometric functions, sec of 80° =
- $\pm\frac{1}{\sqrt{1 – \sin^{2} 80^\circ}}$
- $\pm \sqrt{1+\tan^{2} 80 ^\circ}$
- $\pm\frac{\csc 80^\circ}{\sqrt{\csc^{2} 80^\circ – 1}}$
- $\frac{1}{\cos 80^\circ}$
- $\pm\frac{\sqrt{1+\cot^{2} 80^\circ} }{\cot 80^\circ}$
As the secant function is the reciprocal of the cosine function, 1 / cos 80° = sec80°.
In the next part we discuss the trigonometric significance of sec80°, and there you can also learn what the search calculations form in the sidebar is used for.
What is sec 80°?
In a triangle which has one angle of 90 degrees, the secant of the angle of 80° is the ratio of the length of the hypotenuse h to the length of the adjacent side a: sec 80° = h/a.
In a circle with the radius r, the horizontal axis x, and the vertical axis y, 80 degrees is the angle formed by the two sides x and r; r moving counterclockwise is the positive angle.
As detailed in the unit-circle definition on our homepage, assumed r = 1, in the intersection of the point (x,y) and the circle, x = cos 80°.
Bringing together the triangle definition and the unit circle definition of secant 80 degrees, a = x and h = r = 1. It follows that $1/x\hspace{5px} =\hspace{5px}\frac{hypotenuse}{adjacent}\hspace{5px}=\hspace{5px}\sec 80^\circ$.
Note that you can locate many terms including the secant80° value using the search form. On mobile devices you can find it by scrolling down. Enter, for instance, value of sec80°.
Along the same lines, using the aforementioned form, can you look up terms such as sec 80° value, sec 80, sec80° value and what is the sec of 80 degrees, just to name a few.
Given the periodic property of secant of 80°, to determine the secant of an angle > 360°, e.g. 800°, calculate sec 800° as sec (800 Mod 360)° = secant of 80°, or use our form.
Conclusion
The frequently asked questions in the context include what is sec 80 degrees and what is the sec of 80 degrees for example; reading our content they are no-brainers.
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– Article written by Mark, last updated on February 19th, 2017