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Welcome to sec pi/4, our post aboutthe secant of pi/4.
For the secant of pi/4 we use the abbreviation sec for the trigonometric function and write it as sec pi/4.
If you have been looking for what is sec pi/4, or if you have been wondering about sec pi/4 radians in degrees, then you are right here, too.
In this post you can find the sec pi/4 value, along with identities.
Read on to learn all about the sec of pi/4.
Sec Pi/4 Radians
If you want to know what is sec pi/4 radians 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 pi/4:
sec pi/4 = √2
sec pi/4 radians = √2
The sec of pi/4 radians is √2, the same as sec of pi/4 radians in degrees. To change pi/4 radians to degrees multiply pi/4 by 180° / $\pi$ = 45°. Sec pi/4 = sec 45 degrees.
Our results of secpi/4 have been rounded to five decimal places. If you want secant pi/4 with higher accuracy, then use the calculator below; our tool displays ten decimal places.
To calculate sec pi/4 radians insert the angle pi/4 in decimal notation, but if you want to calculate sec pi/4 in degrees, then you have to press the swap unit button first.
Calculate sec [radians]
Note that secpi/4 is periodic: sec (pi/4 + n × 2pi) = sec pi/4, n$\hspace{5px} \in \hspace{5px} \mathbb{Z}$.
In terms of the other five trigonometric functions, sec of pi/4 =
- $\pm\frac{1}{\sqrt{1 – \sin^{2} \pi/4}}$
- $\pm \sqrt{1+\tan^{2} \pi/4 }$
- $\pm\frac{\csc \pi/4}{\sqrt{\csc^{2} (\pi/4) – 1}}$
- $\frac{1}{\cos \pi/4}$
- $\pm\frac{\sqrt{1+\cot^{2} \pi/4} }{\cot \pi/4}$
As the secant function is the reciprocal of the cosine function, 1 / cos pi/4 = secpi/4.
In the next part we discuss the trigonometric significance of secpi/4, and there you can also learn what the search calculations form in the sidebar is used for.
What is sec Pi/4?
In a triangle which has one angle of pi/2, the secant of the angle of pi/4 is the ratio of the length of the hypotenuse h to the length of the adjacent side a: sec pi/4 = h/a.
In a circle with the radius r, the horizontal axis x, and the vertical axis y, pi/4 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 pi/4.
Bringing together the triangle definition and the unit circle definition of secant pi/4, a = x and h = r = 1. It follows that $1/x\hspace{5px} =\hspace{5px}\frac{hypotenuse}{adjacent}\hspace{5px}=\hspace{5px}\sec \pi/4$.
Note that you can locate many terms including the secantpi/4 value using the search form. On mobile devices you can find it by scrolling down. Enter, for instance, value of secpi/4.
Along the same lines, using the aforementioned form, can you look up terms such as sec pi/4 value, sec pi/4, secpi/4 value and what is the sec of pi/4 radians, just to name a few.
Given the periodic property of secant of pi/4, to determine the secant of an angle > 2pi, e.g. 17/4 pi, calculate sec 17/4 pi as sec (17/4 pi mod 2pi) = secant of pi/4, or use our form.
Conclusion
The frequently asked questions in the context include what is sec pi/4 radians and what is the sec of pi/4 radians for example; reading our content they are no-brainers.
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– Article written by Mark, last updated on February 26th, 2017