Table of Contents
Welcome to cos pi/4, our post aboutthe cosine of pi/4.
For the cosine of pi/4 we use the abbreviation cos for the trigonometric function and write it as cos pi/4.
If you have been looking for what is cos pi/4, or if you have been wondering about cos pi/4 radians in degrees, then you are right here, too.
In this post you can find the cos pi/4 value, along with identities.
Read on to learn all about the cos of pi/4.
Cos Pi/4 Radians
If you want to know what is cos 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 cos pi/4:
cos pi/4 = √(2)/2
cos pi/4 radians = √(2)/2
The cos of pi/4 radians is √(2)/2, the same as cos of pi/4 radians in degrees. To change pi/4 radians to degrees multiply pi/4 by by 180° / $\pi$ = 45°. Cos pi/4 = cos 45 degrees.
Our results of cospi/4 have been rounded to five decimal places. If you want cosine pi/4 with higher accuracy, then use the calculator below; our tool displays ten decimal places.
To calculate cos pi/4 radians insert the angle pi/4 in decimal notation, but if you want to calculate cos pi/4 in degrees, then you have to press the swap unit button first.
Calculate cos [radians]
The identities of cosine pi/4 are as follows:
= sin (pi/2 + pi/4) = sin 3/4 pi
= sin (pi/2 – pi/4) = sin 1/4 pi
-cospi/4
= cos (pi + pi/4) = cos 5/4 pi
= cos (pi – pi/4) = cos 3/4 pi
There are more formulas for the double angle (2 × pi/4), half angle ((pi/4/2)) as well as the sum, difference and products of two angles such as pi/4 and β.
You can locate all of them in the respective article found in the header menu. To find everything about cos -pi/4 click the link. And here is all about sin pi/4, including, for instance, a converter.
In terms of the other five trigonometric functions, cos of pi/4 =
- $\pm \sqrt{1-\sin^{2} \pi/4 }$
- $\pm\frac{1}{\sqrt{1 + \tan^{2} \pi/4}}$
- $\pm\frac{\cot \pi/4}{\sqrt{1 + \cot^{2} \pi/4}}$
- $\frac{1}{\sec \pi/4}$
- $\pm\frac{\sqrt{\csc^{2} (\pi/4) – 1} }{\csc \pi/4}$
As the cosine function is the reciprocal of the secant function, 1 / sec pi/4 = cospi/4.
In the next part we discuss the trigonometric significance of cospi/4, and there you can also learn what the search calculations form in the sidebar is used for.
What is cos Pi/4?
In a triangle which has one angle of pi/2, the cosine of the angle of pi/4 is the ratio of the length of the adjacent side a to the length of the hypotenuse h: cos pi/4 = a/h.
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 cosine pi/4, a = x and h = r = 1. It follows that $x\hspace{5px} =\hspace{5px}\frac{adjacent}{hypotenuse}\hspace{5px}=\hspace{5px}\cos \pi/4$.
Note that you can locate many terms including the cosinepi/4 value using the search form. On mobile devices you can find it by scrolling down. Enter, for instance, value of cospi/4.
Along the same lines, using the aforementioned form, can you look up terms such as cos pi/4 value, cos pi/4, cospi/4 value and what is the cos of pi/4 radians, just to name a few.
Given the periodic property of cosine of pi/4, to determine the cosine of an angle > 2pi, e.g. 17/4 pi, calculate cos 17/4 pi as cos (17/4 pi mod 2pi) = cosine of pi/4, or look it up with our form.
Conclusion
The frequently asked questions in the context include what is cos pi/4 radians and what is the cos of pi/4 degrees for example; reading our content they are no-brainers.
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– Article written by Mark, last updated on February 26th, 2017