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Welcome to cos 75°, our post aboutthe cosine of 75 degrees.
For the cosine of 75 degrees we use the abbreviation cos for the trigonometric function together with the degree symbol °, and write it as cos 75°.
If you have been looking for what is cos 75°, or if you have been wondering about cos 75 degrees in radians, then you are right here, too.
In this post you can find the cos 75° value, along with identities.
Read on to learn all about the cos of 75°.
Cos 75 Degrees
If you want to know what is cos 75 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 75°:
cos 75° = (√6-√2)/4
cos 75 degrees = (√6-√2)/4
The cos of 75 degrees is (√6-√2)/4, the same as cos of 75 degrees in radians. To obtain 75 degrees in radian multiply 75° by $\pi$ / 180° = 5/12 $\pi$. Cos 75degrees = cos (5/12 × $\pi)$.
Our results of cos75° have been rounded to five decimal places. If you want cosine 75° with higher accuracy, then use the calculator below; our tool displays ten decimal places.
To calculate cos 75 degrees insert the angle 75 in the field labelled °, but if you want to calculate cos 75 in radians, then you have to press the swap unit button first.
Calculate cos [degrees]
The identities of cosine 75° are as follows:
= sin (90°+75°) = sin 165°
= sin (90°-75°) = sin 15°
-cos75°
= cos (180°+75°) = cos 255°
= cos (180°-75°) = cos 105°
There are more formulas for the double angle (2 × 75°), half angle ((75/2)°) as well as the sum, difference and products of two angles such as 75° and β.
You can locate all of them in the respective article found in the header menu. To find everything about cos -75° click the link. And here is all about sin 75°, including, for instance, a converter.
In terms of the other five trigonometric functions, cos of 75° =
- $\pm \sqrt{1-\sin^{2} 75 ^\circ}$
- $\pm\frac{1}{\sqrt{1 + \tan^{2} 75^\circ}}$
- $\pm\frac{\cot 75^\circ}{\sqrt{1 + \cot^{2} 75^\circ}}$
- $\frac{1}{\sec 75^\circ}$
- $\pm\frac{\sqrt{\csc^{2} 75^\circ – 1} }{\csc 75^\circ}$
As the cosine function is the reciprocal of the secant function, 1 / sec 75° = cos75°.
In the next part we discuss the trigonometric significance of cos75°, and there you can also learn what the search calculations form in the sidebar is used for.
What is cos 75°?
In a triangle which has one angle of 90 degrees, the cosine of the angle of 75° is the ratio of the length of the adjacent side a to the length of the hypotenuse h: cos 75° = a/h.
In a circle with the radius r, the horizontal axis x, and the vertical axis y, 75 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 75°.
Bringing together the triangle definition and the unit circle definition of cosine 75 degrees, a = x and h = r = 1. It follows that $x\hspace{5px} =\hspace{5px}\frac{adjacent}{hypotenuse}\hspace{5px}=\hspace{5px}\cos 75^\circ$.
Note that you can locate many terms including the cosine75° value using the search form. On mobile devices you can find it by scrolling down. Enter, for instance, value of cos75°.
Along the same lines, using the aforementioned form, can you look up terms such as cos 75° value, cos 75, cos75° value and what is the cos of 75 degrees, just to name a few.
Given the periodic property of cosine of 75°, to determine the cosine of an angle > 360°, e.g. 795°, calculate cos 795° as cos (795 Mod 360)° = cosine of 75°, or look it up with our form.
Conclusion
The frequently asked questions in the context include what is cos 75 degrees and what is the cos of 75 degrees for example; reading our content they are no-brainers.
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– Article written by Mark, last updated on February 26th, 2017