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Sin 10°

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°:

sin10° = 0.17365
sin 10° = 0.17365
sin 10 degrees = 0.17365

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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]

A Really Cool Sine Calculator and Useful Information! Please ReTweet. Click To TweetBesides sin10°, similar trigonometric calculations on our site include, but are not limited, to:

The identities of sine 10° are as follows:

= cos (90°-10°) = cos 80°
= sin (180°-10°) = sin 170°

= cos (90°+10°) = cos 100°
= sin (180°+10°) = sin 190°

Note that sin10° is periodic: sin (10° + n × 360°) = sin 10 degrees, n$\hspace{5px} \in \hspace{5px} \mathbb{Z}$.

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.


Sin 10°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.

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