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Welcome to sin 36°, our post aboutthe sine of 36 degrees.
For the sine of 36 degrees we use the abbreviation sin for the trigonometric function together with the degree symbol °, and write it as sin 36°.
If you have been looking for what is sin 36°, or if you have been wondering about sin 36 degrees in radians, then you are right here, too.
In this post you can find the sin 36° value, along with identities.
Read on to learn all about the sin of 36°.
Sin 36 Degrees
If you want to know what is sin 36 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 36°:
sin 36° = 0.58779
sin 36 degrees = 0.58779
The sin of 36 degrees is 0.58779, the same as sin of 36 degrees in radians. To obtain 36 degrees in radian multiply 36° by $\pi$ / 180° = 1/5 $\pi$. Sin 36degrees = sin (1/5 × $\pi)$.
Our results of sin36° have been rounded to five decimal places. If you want sine 36° with higher accuracy, then use the calculator below; our tool displays ten decimal places.
To calculate sin 36 degrees insert the angle 36 in the field labelled °, but if you want to calculate sin 36 in radians, then you have to press the swap unit button first.
Calculate sin [degrees]
The identities of sine 36° are as follows:
= cos (90°-36°) = cos 54°
= sin (180°-36°) = sin 144°
-sin36°
= cos (90°+36°) = cos 126°
= sin (180°+36°) = sin 216°
There are more formulas for the double angle (2 × 36°), half angle ((36/2)°) as well as the sum, difference and products of two angles such as 36° and β.
You can locate all of them in the respective article found in the header menu. To find everything about sin -36° click the link. And here is all about cos 36°, including, for instance, a converter.
In terms of the other five trigonometric functions, sin of 36° =
- $\pm \sqrt{1-\cos^{2} 36 ^\circ}$
- $\pm\frac{\tan 36^\circ}{\sqrt{1 + \tan^{2} 36^\circ}}$
- $\pm\frac{1}{\sqrt{1 + \cot^{2} 36^\circ}}$
- $\pm\frac{\sqrt{\sec^{2} 36^\circ – 1} }{\sec 36^\circ}$
- $\frac{1}{\csc 36^\circ}$
As the cosecant function is the reciprocal of the sine function, 1 / csc 36° = sin36°.
In the next part of this article of this article we discuss the trigonometric significance of sin36°, and there you can also learn what the search calculations form in the sidebar is used for.
What is sin 36°?
In a triangle which has one angle of 90 degrees, the sine of the angle of 36° is the ratio of the length of the opposite side o to the length of the hypotenuse h: sin 36° = o/h.
In a circle with the radius r, the horizontal axis x, and the vertical axis y, 36 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 36°.
Bringing together the triangle definition and the unit circle definition of sine 36 degrees, o = y and h = r = 1. It follows that $y\hspace{5px} =\hspace{5px}\frac{opposite}{hypotenuse}\hspace{5px}=\hspace{5px}\sin 36^\circ$.
Note that you can locate many terms including the sine36° value using the search form. On mobile devices you can find it by scrolling down. Enter, for instance, value of sin36°.
Along the same lines, using the aforementioned form, can you look up terms such as sin 36° value, sin 36, sin36° value and what is the sin of 36 degrees, just to name a few.
Given the periodic property of sine of 36°, to determine the sine of an angle > 360°, e.g. 756°, calculate sin 756° as sin (756 Mod 360)° = sine of 36°, or look it up with our form.
Conclusion
The frequently asked questions in the context include what is sin 36 degrees and what is the sin of 36 degrees for example; reading our content they are no-brainers.
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– Article written by Mark, last updated on February 16th, 2017