Table of Contents
Welcome to sin 10°, our post aboutthe sine of 10 degrees.
For the sine of 10 degrees we use the abbreviation sin for the trigonometric function together with the degree symbol °, and write it as sin 10°.
If you have been looking for what is sin 10°, or if you have been wondering about sin 10 degrees in radians, then you are right here, too.
In this post you can find the sin 10° value, along with identities.
Read on to learn all about the sin of 10°.
Sin 10 Degrees
If you want to know what is sin 10 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 sin 10°:
sin 10° = 0.17365
sin 10 degrees = 0.17365
The sin of 10 degrees is 0.17365, the same as sin of 10 degrees in radians. To obtain 10 degrees in radian multiply 10° by $\pi$ / 180° = 1/18 $\pi$. Sin 10degrees = sin (1/18 × $\pi)$.
Our results of sin10° have been rounded to five decimal places. If you want sine 10° with higher accuracy, then use the calculator below; our tool displays ten decimal places.
To calculate sin 10 degrees insert the angle 10 in the field labelled °, but if you want to calculate sin 10 in radians, then you have to press the swap unit button first.
Calculate sin [degrees]
The identities of sine 10° are as follows:
= cos (90°-10°) = cos 80°
= sin (180°-10°) = sin 170°
-sin10°
= cos (90°+10°) = cos 100°
= sin (180°+10°) = sin 190°
There are more formulas for the double angle (2 × 10°), half angle ((10/2)°) as well as the sum, difference and products of two angles such as 10° and β.
You can locate all of them in the respective article found in the header menu. To find everything about sin -10° click the link. And here is all about cos 10°, including, for instance, a converter.
In terms of the other five trigonometric functions, sin of 10° =
- $\pm \sqrt{1-\cos^{2} 10 ^\circ}$
- $\pm\frac{\tan 10^\circ}{\sqrt{1 + \tan^{2} 10^\circ}}$
- $\pm\frac{1}{\sqrt{1 + \cot^{2} 10^\circ}}$
- $\pm\frac{\sqrt{\sec^{2} 10^\circ – 1} }{\sec 10^\circ}$
- $\frac{1}{\csc 10^\circ}$
As the cosecant function is the reciprocal of the sine function, 1 / csc 10° = sin10°.
In the next part of this article of this article we discuss the trigonometric significance of sin10°, and there you can also learn what the search calculations form in the sidebar is used for.
What is sin 10°?
In a triangle which has one angle of 90 degrees, the sine of the angle of 10° is the ratio of the length of the opposite side o to the length of the hypotenuse h: sin 10° = o/h.
In a circle with the radius r, the horizontal axis x, and the vertical axis y, 10 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, y = sin 10°.
Bringing together the triangle definition and the unit circle definition of sine 10 degrees, o = y and h = r = 1. It follows that $y\hspace{5px} =\hspace{5px}\frac{opposite}{hypotenuse}\hspace{5px}=\hspace{5px}\sin 10^\circ$.
Note that you can locate many terms including the sine10° value using the search form. On mobile devices you can find it by scrolling down. Enter, for instance, value of sin10°.
Along the same lines, using the aforementioned form, can you look up terms such as sin 10° value, sin 10, sin10° value and what is the sin of 10 degrees, just to name a few.
Given the periodic property of sine of 10°, to determine the sine of an angle > 360°, e.g. 730°, calculate sin 730° as sin (730 Mod 360)° = sine of 10°, or look it up with our form.
Conclusion
The frequently asked questions in the context include what is sin 10 degrees and what is the sin of 10 degrees for example; reading our content they are no-brainers.
But, if there is something else about sine 10° you would like to know, fill in the form on the bottom of this post, or send us an email with a subject line such as sine 10 degrees.
If our calculator and the information on sin10° have been helpful, please hit the sharing buttons to spread the word about our content, and don’t forget to bookmark us.
Or, even better, install absolutely free PWA app (see menu or sidebar)!
Thanks for visiting sin10 degrees.
– Article written by Mark, last updated on February 16th, 2017