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Cos Pi/12

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Welcome to cos pi/12, our post aboutthe cosine of pi/12.

For the cosine of pi/12 we use the abbreviation cos for the trigonometric function and write it as cos pi/12.

If you have been looking for what is cos pi/12, or if you have been wondering about cos pi/12 radians in degrees, then you are right here, too.

In this post you can find the cos pi/12 value, along with identities.

Read on to learn all about the cos of pi/12.

Cos Pi/12 Radians

If you want to know what is cos pi/12 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/12:

cospi/12 = (√6+√2)/4
cos pi/12 = (√6+√2)/4
cos pi/12 radians = (√6+√2)/4

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The cos of pi/12 radians is (√6+√2)/4, the same as cos of pi/12 radians in degrees. To change pi/12 radians to degrees multiply pi/12 by by 180° / $\pi$ = 15°. Cos pi/12 = cos 15 degrees.

Our results of cospi/12 have been rounded to five decimal places. If you want cosine pi/12 with higher accuracy, then use the calculator below; our tool displays ten decimal places.

To calculate cos pi/12 radians insert the angle pi/12 in decimal notation, but if you want to calculate cos pi/12 in degrees, then you have to press the swap unit button first.

Calculate cos [radians]

A Really Cool Cosine Calculator and Useful Information! Please ReTweet. Click To TweetBesides cospi/12, similar trigonometric calculations on our site include, but are not limited, to:

The identities of cosine pi/12 are as follows:

= sin (pi/2 + pi/12) = sin 7/12 pi
= sin (pi/2 – pi/12) = sin 5/12 pi

= cos (pi + pi/12) = cos 13/12 pi
= cos (pi – pi/12) = cos 11/12 pi

Note that cospi/12 is periodic: cos (pi/12 + n × 2pi) = cos pi/12, n$\hspace{5px} \in \hspace{5px} \mathbb{Z}$.

There are more formulas for the double angle (2 × pi/12), half angle ((pi/12/2)) as well as the sum, difference and products of two angles such as pi/12 and β.

You can locate all of them in the respective article found in the header menu. To find everything about cos -pi/12 click the link. And here is all about sin pi/12, including, for instance, a converter.

In terms of the other five trigonometric functions, cos of pi/12 =

  • $\pm \sqrt{1-\sin^{2} \pi/12 }$
  • $\pm\frac{1}{\sqrt{1 + \tan^{2} \pi/12}}$
  • $\pm\frac{\cot \pi/12}{\sqrt{1 + \cot^{2} \pi/12}}$
  • $\frac{1}{\sec \pi/12}$
  • $\pm\frac{\sqrt{\csc^{2} (\pi/12) – 1} }{\csc \pi/12}$

As the cosine function is the reciprocal of the secant function, 1 / sec pi/12 = cospi/12.

In the next part we discuss the trigonometric significance of cospi/12, and there you can also learn what the search calculations form in the sidebar is used for.

What is cos Pi/12?

In a triangle which has one angle of pi/2, the cosine of the angle of pi/12 is the ratio of the length of the adjacent side a to the length of the hypotenuse h: cos pi/12 = a/h.

In a circle with the radius r, the horizontal axis x, and the vertical axis y, pi/12 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/12.

Bringing together the triangle definition and the unit circle definition of cosine pi/12, a = x and h = r = 1. It follows that $x\hspace{5px} =\hspace{5px}\frac{adjacent}{hypotenuse}\hspace{5px}=\hspace{5px}\cos \pi/12$.

Note that you can locate many terms including the cosinepi/12 value using the search form. On mobile devices you can find it by scrolling down. Enter, for instance, value of cospi/12.

Along the same lines, using the aforementioned form, can you look up terms such as cos pi/12 value, cos pi/12, cospi/12 value and what is the cos of pi/12 radians, just to name a few.

Given the periodic property of cosine of pi/12, to determine the cosine of an angle > 2pi, e.g. 49/12 pi, calculate cos 49/12 pi as cos (49/12 pi mod 2pi) = cosine of pi/12, or look it up with our form.


The frequently asked questions in the context include what is cos pi/12 radians and what is the cos of pi/12 degrees for example; reading our content they are no-brainers.

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