The implementation can be found here(*).
The sin function is approximated by a 13-degree polynomial. That is, a function on the shape
c12x12 + c11x11 + ... + c1x1 + c0x0
on the interval [0,ฯ/4]
The description of the algorithm looks as follows:
33 * Algorithm
34 * 1. Since sin(-x) = -sin(x), we need only to consider positive x.
35 * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
36 * 3. sin(x) is approximated by a polynomial of degree 13 on
37 * [0,pi/4]
38 * 3 13
39 * sin(x) ~ x + S1*x + ... + S6*x
40 * where
41 *
42 * |sin(x) 2 4 6 8 10 12 | -58
43 * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2
44 * | x |
45 *
46 * 4. sin(x+y) = sin(x) + sin'(x')*y
47 * ~ sin(x) + (1-x*x/2)*y
48 * For better accuracy, let
49 * 3 2 2 2 2
50 * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
51 * then 3 2
52 * sin(x) = x + (S1*x + (x *(r-y/2)+y))
53 */
(*) Disclamer: Talking about OpenJDK here
Answer from aioobe on Stack OverflowW3Schools
w3schools.com โบ java โบ ref_math_sin.asp
Java Math sin() Method
Java Examples Java Videos Java ... ... System.out.println(Math.sin(3)); System.out.println(Math.sin(-3)); System.out.println(Math.sin(0)); System.out.println(Math.sin(Math.PI)); System.out.println(Math.sin(Math.PI/2));...
Programiz
programiz.com โบ java-programming โบ library โบ math โบ sin
Java Math sin()
Note: If the argument is zero, then the result of the sin() method is also zero with the same sign as the argument. import java.lang.Math; class Main { public static void main(String[] args) { // create variable in Degree double a = 30; double b = 45; // convert to radians a = Math.toRadians(a); b = Math.toRadians(b); // print the sine value System.out.println(Math.sin(a)); // 0.49999999999999994 System.out.println(Math.sin(b)); // 0.7071067811865475 // sin() with 0 as its argument System.out.println(Math.sin(0.0)); // 0.0 } }
math - How is sine implemented in Java? - Stack Overflow
I found this question about sin in Java, but that's asking why the sin function isn't wrapped in native code. I'm asking something entirely different. I want to know how the function was implemented. (Since it's wrapped in native code, I can't see it.) Did they simply implement it from the Taylor series expansion: ... I can't look at the code for the Math.sine() function, since it gets wrapped up in native code. ... Math.PI is a constant. ... Try Googling for "fdlibm source... More on stackoverflow.com
Differences between Math.sin() and StrictMath.sin()
JVM generates native platform specific code in Math. Modern processors have separate instructions for many trigonometry functions, those are much faster. JVM makes use of them if possible. StrictMath is the "default" if those native don't exist. And it does the math in software. (hence the slower runtime) More on reddit.com
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June 29, 2013Java's 13th order polynomial has somehow beat my third-order polynomial in computational efficiency. How did they do it?
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June 1, 2023I translated the C Donut source code into Java because I was bored
You should try making this a donut shape too, Java will allow it! You can shorten some expressions by doing static imports (e.g. import static java.lang.System.out, import static java.lang.Math.sin, etc.) More on reddit.com
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July 6, 2020Videos
Mastering Java, Vol 2 Lesson 19 Sin, Cos, And Tangent 11
02:01
Mastering Java, Vol 2 Lesson 19 Sin, Cos, And Tangent - YouTube
06:18
Java Tutorial - 19 - Sin, Cos, and Tangent (Math Functions) - YouTube
11:14
Sine method in Java - YouTube
Java Tutorial - 19 - Sin, Cos, and Tangent (Math Functions) - Math ...
15:30
Java Math methods | Java trigonometry methods | Java Random Number ...
GeeksforGeeks
geeksforgeeks.org โบ java โบ java-math-sin-method-examples
Java Math sin() method with Examples - GeeksforGeeks
July 11, 2025 - // Java program to demonstrate working // of java.lang.Math.sin() method import java.lang.Math; class Gfg { // driver code public static void main(String args[]) { double a = 30; // converting values to radians double b = Math.toRadians(a); System.out.println(Math.sin(b)); a = 45; // converting values to radians b = Math.toRadians(a); System.out.println(Math.sin(b)); a = 60; // converting values to radians b = Math.toRadians(a); System.out.println(Math.sin(b)); a = 90; // converting values to radians b = Math.toRadians(a); System.out.println(Math.sin(b)); } }
Tabnine
tabnine.com โบ home page โบ code โบ java โบ java.lang.math
java.lang.Math.sin java code examples | Tabnine
* @param radians the angle in radians */ public Vector2 rotateRad (float radians) { float cos = (float)Math.cos(radians); float sin = (float)Math.sin(radians); float newX = this.x * cos - this.y * sin; float newY = this.x * sin + this.y * cos; ...
Scaler
scaler.com โบ home โบ topics โบ java math sin()
Java Math sin() | Scaler Topics
April 14, 2024 - The built-in java.lang.Math.sin() function returns the sine value of the argument supplied. The argument is expected to be in radians. If the argument is NaN (Not-a-Number) or infinity, the function will return NaN as the outcome.
GeeksforGeeks
geeksforgeeks.org โบ java โบ trigonometric-functions-in-java-with-examples
Trigonometric Functions in Java with Examples - GeeksforGeeks
December 29, 2025 - Example 1 : Program demonstrating ... radians = Math.toRadians(degrees); // sin() method to get the sine value double sinValue = Math.sin(radians); // prints the sine value System.out.println("sin(" + degrees + ") = " + sinValue); ...
Tutorialspoint
tutorialspoint.com โบ java โบ number_sin.htm
Java - sin() Method
September 30, 2019 - public class Test { public static void main(String args[]) { double degrees = 45.0; double radians = Math.toRadians(degrees); System.out.format("The value of pi is %.4f%n", Math.PI); System.out.format("The sine of %.1f degrees is %.4f%n", degrees, Math.sin(radians)); } } This will produce the ...
Reddit
reddit.com โบ r/java โบ differences between math.sin() and strictmath.sin()
r/java on Reddit: Differences between Math.sin() and StrictMath.sin()
June 29, 2013 -
...besides the obvious? So a couple years ago I was working on a hobby project and I had to use sin() a lot (it could be several billions of calls). So I was looking at ways to speed it up. One of the things I did was to look at the source. Math.sin's (which I was using) body was:
public static double sin(double a)
{
return StrictMath.sin(a);
}
So I thought, why not just use StrictMath.sin() instead and save a call/return? Turns out the execution time increased, every time. I asked my professor and he didn't know. So I asked the java forums, and I never got a definite answer. So now I figure I'll ask here as the thought came up. Does anyone know? I assume there's some trickery going on (like the source for Math.java isn't the actual implementation or some such).
Top answer 1 of 5
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JVM generates native platform specific code in Math. Modern processors have separate instructions for many trigonometry functions, those are much faster. JVM makes use of them if possible. StrictMath is the "default" if those native don't exist. And it does the math in software. (hence the slower runtime)
2 of 5
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From the Java6 Java docs By default many of the Math methods simply call the equivalent method in StrictMath for their implementation. Code generators are encouraged to use platform-specific native libraries or microprocessor instructions, where available, to provide higher-performance implementations of Math methods. This suggests that the JVM could be using a native function to calculate Math.sin rather than StrictMath.sin
Vultr Docs
docs.vultr.com โบ java โบ standard-library โบ java โบ lang โบ Math โบ sin
Java Math sin() - Calculate Sine Value | Vultr Docs
December 3, 2024 - This code snippet converts 90 degrees to radians and calculates the sine value. The Math.sin() method requires the angle in radians, thus necessitating the conversion.
Tutorialspoint
tutorialspoint.com โบ java โบ lang โบ math_sin.htm
Java - Math tan(double x) method
March 24, 2009 - package com.tutorialspoint; public class MathDemo { public static void main(String[] args) { // get a double number double x = 45.0; // convert it to radian x = Math.toRadians(x); // print the trigonometric sine for this double System.out.println("Math.sin(" + x + ")=" + Math.sin(x)); } }
Baeldung
baeldung.com โบ home โบ algorithms โบ using math.sin with degrees
Using Math.sin with Degrees | Baeldung
January 25, 2024 - Whenever we are using any of Javaโs trigonometric functions, we should first think about what is the unit of our input. We can see this principle in action by taking a look at the Math.sin method, one of the many that Java provides:
Codecademy
codecademy.com โบ docs โบ java โบ math methods โบ .sin()
Java | Math Methods | .sin() | Codecademy
July 28, 2021 - The Math.sin() method returns the trigonometric sine of an angle argument, given in radians. ... Looking for an introduction to the theory behind programming? Master Python while learning data structures, algorithms, and more! ... Learn to code in Java โ a robust programming language used ...
BeginnersBook
beginnersbook.com โบ 2022 โบ 10 โบ java-math-sin-method
Java Math.sin() Method
December 17, 2022 - public class JavaExample { public static void main(String[] args) { double degrees = -90; double degrees2 = 90; double degrees3 = 180; double degrees4 = -180; System.out.println(Math.sin(Math.toRadians(degrees))); System.out.println(Math.sin(Math.toRadians(degrees2))); System.out.println(M...
Princeton CS
introcs.cs.princeton.edu โบ java โบ 13flow โบ Sin.java.html
Sin.java
December 2, 2024 - * ******************************************************************************/ public class Sin { public static void main(String[] args) { double x = Double.parseDouble(args[0]); // convert x to an angle between -2 PI and 2 PI x = x % (2 * Math.PI); // compute the Taylor series approximation ...
AlphaCodingSkills
alphacodingskills.com โบ java โบ notes โบ java-math-sin.php
Java Math sin() Method - AlphaCodingSkills
June 17, 2012 - In the example below, sin() method ... of an angle. import java.lang.*; public class MyClass { public static void main(String[] args) { System.out.println(Math.sin(Math.PI/6)); System.out.println(Math.sin(Math.PI/4)); System.out.println(Math.sin(Math.PI/3)); } }...
PREP INSTA
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Java Math sin() Method | prepinsta
July 20, 2023 - public class Main{ public static void main(String[] args) { double angle = Math.toRadians(30); // convert degrees to radians double sine = Math.sin(angle); // calculate sine of angle System.out.println("Sine of 30 degrees: " + sine); } } ... ...
Java Tutorial HQ
javatutorialhq.com โบ java tutorial โบ java.lang โบ math โบ sin() method example
Java Math sin() method example
September 30, 2019 - Below is a java code demonstrates the use of sin() method of Math class. The example presented might be simple however it shows the behaviour of the sin() method. package com.javatutorialhq.java.examples; import java.util.Scanner; /* * This example source code demonstrates the use of * sin() method of Math class */ public class MathSineExample { public static void main(String[] args) { // Ask for user input System.out.print("Enter an angle in degrees:"); // use scanner to read the console input Scanner scan = new Scanner(System.in); // Assign the user to String variable String s = scan.nextLin
Wikitechy
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java tutorial - Java Math.sin() Method - By Microsoft Award MVP - tutorial java - java programming - learn java - java basics - java for beginners - Learn in 30sec | wikitechy
java math.cos degree example java math sin Source code java math.sin the degree of java for radians sin in radians java math sin () in java
Tutorial Gateway
tutorialgateway.org โบ java-sin-function
Java sin Function
March 28, 2025 - Java sin function is a Math Library function that is used to calculate the Trigonometry Sine for given expression. Syntax Math.sin (double x)