For the cosine of 45 degrees we use the abbreviation cos for the trigonometric function together with the degree symbol °, and write it as cos 45°.

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If you have been looking for what is cos 45°, or if you have been wondering about cos 45 degrees in radians, then you are right here, too.

In this post you can find the cos 45° value, along with identities.

Read on to learn all about the cos of 45°.

Cos 45 Degrees

If you want to know what is cos 45 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 cos 45°:

cos45° = √(2)/2cos 45° = √(2)/2cos 45 degrees = √(2)/2" onclick="if (!window.__cfRLUnblockHandlers) return false; return fbs_click()" target="_blank" rel="nofollow noopener noreferrer" data-cf-modified-74cc272e46fabc14c79fed21-="">Share on Facebook

The cos of 45 degrees is √(2)/2, the same as cos of 45 degrees in radians. To obtain 45 degrees in radian multiply 45° by $pi$ / 180° = 1/4 $pi$. Cos 45degrees = cos (1/4 × $pi)$.

Our results of cos45° have been rounded to five decimal places. If you want cosine 45° with higher accuracy, then use the calculator below; our tool displays ten decimal places.

To calculate cos 45 degrees insert the angle 45 in the field labelled °, but if you want to calculate cos 45 in radians, then you have to press the swap unit button first.

Calculate cos


° :
A Really Cool Cosine Calculator and Useful Information! Please ReTweet. Click To TweetBesides cos45°, similar trigonometric calculations on our site include, but are not limited, to:

The identities of cosine 45° are as follows:cos45°= sin (90°+45°) = sin 135°= sin (90°-45°) = sin 45°

-cos45°= cos (180°+45°) = cos 225°= cos (180°-45°) = cos 135°Note that cos45° is periodic: cos (45° + n × 360°) = cos 45 degrees, n$hspace5px in hspace5px mathbbZ$.

There are more formulas for the double angle (2 × 45°), half angle ((45/2)°) as well as the sum, difference and products of two angles such as 45° and β.

You can locate all of them in the respective article found in the header menu. To find everything about cos -45° click the link. And here is all about sin 45°, including, for instance, a converter.

In terms of the other five trigonometric functions, cos of 45° =

$pm sqrt1-sin^2 45 ^circ$ $pmfrac1sqrt1 + an^2 45^circ$ $pmfraccot 45^circsqrt1 + cot^2 45^circ$ $frac1sec 45^circ$ $pmfracsqrtcsc^2 45^circ – 1 csc 45^circ$

As the cosine function is the reciprocal of the secant function, 1 / sec 45° = cos45°.

In the next part we discuss the trigonometric significance of cos45°, and there you can also learn what the search calculations form in the sidebar is used for.

What is cos 45°?

In a triangle which has one angle of 90 degrees, the cosine of the angle of 45° is the ratio of the length of the adjacent side a to the length of the hypotenuse h: cos 45° = a/h.

In a circle with the radius r, the horizontal axis x, and the vertical axis y, 45 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 45°.

Bringing together the triangle definition and the unit circle definition of cosine 45 degrees, a = x and h = r = 1. It follows that $xhspace5px =hspace5pxfracadjacenthypotenusehspace5px=hspace5pxcos 45^circ$.

Note that you can locate many terms including the cosine45° value using the search form. On mobile devices you can find it by scrolling down. Enter, for instance, value of cos45°.

Along the same lines, using the aforementioned form, can you look up terms such as cos 45° value, cos 45, cos45° value and what is the cos of 45 degrees, just to name a few.

Given the periodic property of cosine of 45°, to determine the cosine of an angle > 360°, e.g. 765°, calculate cos 765° as cos (765 Mod 360)° = cosine of 45°, or look it up with our form.

Conclusion

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