Table of Contents
Welcome to sin 1°, our post aboutthe sine of 1 degree.
For the sine of 1 degree we use the abbreviation sin for the trigonometric function together with the degree symbol °, and write it as sin 1°.
If you have been looking for what is sin 1°, or if you have been wondering about sin 1 degree in radians, then you are right here, too.
In this post you can find the sin 1° value, along with identities.
Read on to learn all about the sin of 1°.
Sin 1 Degree
If you want to know what is sin 1 degree 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 1°:
sin 1° = 0.01745
sin 1 degree = 0.01745
The sin of 1 degree is 0.01745, the same as sin of 1 degree in radians. To obtain 1 degree in radian multiply 1° by $\pi$ / 180° = 1/180 $\pi$. Sin 1degree = sin (1/180 × $\pi)$.
Our results of sin1° have been rounded to five decimal places. If you want sine 1° with higher accuracy, then use the calculator below; our tool displays ten decimal places.
To calculate sin 1 degree insert the angle 1 in the field labelled °, but if you want to calculate sin 1 in radians, then you have to press the swap unit button first.
Calculate sin [degrees]
The identities of sine 1° are as follows:
= cos (90°-1°) = cos 89°
= sin (180°-1°) = sin 179°
-sin1°
= cos (90°+1°) = cos 91°
= sin (180°+1°) = sin 181°
There are more formulas for the double angle (2 × 1°), half angle ((1/2)°) as well as the sum, difference and products of two angles such as 1° and β.
You can locate all of them in the respective article found in the header menu. To find everything about sin -1° click the link. And here is all about cos 1°, including, for instance, a converter.
In terms of the other five trigonometric functions, sin of 1° =
- $\pm \sqrt{1-\cos^{2} 1 ^\circ}$
- $\pm\frac{\tan 1^\circ}{\sqrt{1 + \tan^{2} 1^\circ}}$
- $\pm\frac{1}{\sqrt{1 + \cot^{2} 1^\circ}}$
- $\pm\frac{\sqrt{\sec^{2} 1^\circ – 1} }{\sec 1^\circ}$
- $\frac{1}{\csc 1^\circ}$
As the cosecant function is the reciprocal of the sine function, 1 / csc 1° = sin1°.
In the next part of this article of this article we discuss the trigonometric significance of sin1°, and there you can also learn what the search calculations form in the sidebar is used for.
What is sin 1°?
In a triangle which has one angle of 90 degrees, the sine of the angle of 1° is the ratio of the length of the opposite side o to the length of the hypotenuse h: sin 1° = o/h.
In a circle with the radius r, the horizontal axis x, and the vertical axis y, 1 degree 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 1°.
Bringing together the triangle definition and the unit circle definition of sine 1 degrees, o = y and h = r = 1. It follows that $y\hspace{5px} =\hspace{5px}\frac{opposite}{hypotenuse}\hspace{5px}=\hspace{5px}\sin 1^\circ$.
Note that you can locate many terms including the sine1° value using the search form. On mobile devices you can find it by scrolling down. Enter, for instance, value of sin1°.
Along the same lines, using the aforementioned form, can you look up terms such as sin 1° value, sin 1, sin1° value and what is the sin of 1 degree, just to name a few.
Given the periodic property of sine of 1°, to determine the sine of an angle > 360°, e.g. 721°, calculate sin 721° as sin (721 Mod 360)° = sine of 1°, or look it up with our form.
Conclusion
The frequently asked questions in the context include what is sin 1 degrees and what is the sin of 1 degree for example; reading our content they are no-brainers.
But, if there is something else about sine 1° 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 1 degrees.
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– Article written by Mark, last updated on February 16th, 2017