1 Answer
Why is this happening?
Trigonometric functions generally expect units in radians, while 90
is in degrees.
This also applies for other functions such as cosine and tangent, not just the sine function.
Most programming languages require trigonometric functions to provide their arguments in radians. This simplifies many things, especially on the implementation side as code may interface with C, which is standardized to expect that its arguments to the trig functions in radians.
It also happens to be that the radians are used very commonly in math as they are a natural unit for angle measurement. This Math.SE question and the answers there go into more detail.
Many programming languages don’t provide facilities to convert degrees to radians or back, but an implementation is easy. You can do so by creating a function like so 🙂
PI = 3.1415926535; // or your programming language's standard library's pi constant
function toRadians(degrees) {
return degrees * (PI / 180);
}
Some programming languages however may provide facilities to make the conversion in its standard library (and this should be preferred over writing a conversion yourself). For example, in Python, this is provided by the math.radians
function. The trigonometric functions themselves generally also say what format they expect their inputs to be in.
>>> import math
>>> math.sin(math.radians(90))
1.0
This is the case in some programming language’s standard libraries, such as Rust, Java, Python, MATLAB, and others.
After you’ve converted from degrees to radians, you can then call the trigonometric functions and get the answers you’re expecting.
What are some examples that I can use?
It is helpful to consult your programming language’s standard library and documentation to see if a function for conversion exists in your programming language before writing your own.
Languages that include a standard library function
python (trig function docs  conversion function docs, see also How can I convert radians to degrees with Python?)
>>> import math
>>> math.sin(math.radians(90))
1.0
java (trig function docs*  conversion function docs)
System.out.println(Math.sin(Math.toRadians(90.0)));
matlab (trig function docs  conversion function docs)
sin(deg2rad(90))
Languages that don’t include a standard library function
#include <stdio.h>
#include <math.h>
float deg2rad(float degrees) {
return (M_PI / 180) * degrees;
}
int main() {
printf("%f", sin(deg2rad(90.0)));
}
#include <cmath>
#include <iostream>
#include <numbers>
float deg2rad(float degrees)
{
return (std::numbers::pi_v<float> / 180) * degrees;
}
int main()
{
std::cout << std::sin(deg2rad(90.0)) << 'n';
}
c# (trig function docs*, see also the Remarks sections on the docs for Sin
, Cos
, Tan
)
using Math;
public static double DegreesToRadians(double degrees)
{
return (Math.PI / 180) * degrees;
}
public static int Main() {
Console.WriteLine(Math.Sin(DegreesToRadians(90.0).ToString());
return 0;
}
javascript (trig function docs on MDN*, specifically the Converting between degrees and radians section, see also How can I get sin, cos, and tan to use degrees instead of radians?)
function degToRad(degrees) {
return degrees * (Math.PI / 180);
}
console.log(Math.sin(degToRad(90)));
^{* This programming language doesn’t group their trig functions together in their documentation. Look for functions named sin, cos, tan, or similar.}
1

1
For C at least, since the standard
sin
function usesdouble
, notfloat
, so should yourdeg2rad
function. You could also introducedeg2radf
(usingfloat
) anddeg2radl
(usinglong double
) by analogy with the trig functions.– jcaron40 mins ago
Does this answer your question? Math.Sin() gives incorrect value
yesterday
@trincot this is intended as a canonical QA pair which is language agnostic. See the question on meta
yesterday
I saw the question on meta; I disagree that a new Q&A is needed.
yesterday
It's a question that is language agnostic as it applies to almost all programming languages. The answers, across all programming languages, come down to about 2 (use the library function to make the conversion or write it yourself).
yesterday
@trincot "I take note that you are saying this topic is not language agnostic" – I genuinely can't fathom the reasoning here. The fact that someone wrote a languagespecific QA pair does not refute that the topic is languageagnostic. Nor does the fact of minor syntactic details, differences in library symbol names etc. (enough that code shown for S, whatever that is, would be invalid in Java) make the topic languagespecific – as users of any programming language can be taught what a radian is and what pi is.
17 hours ago