Mathematics · Precalculus
Sine, Cosine and Tangent Calculator
Calculate sine, cosine and tangent for an angle entered in degrees.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Convert 45° to 0.7853981633974483 radians.
- Evaluate sine = 0.7071067811865475 and cosine = 0.7071067811865476.
- Tangent = 0.7071067811865475 ÷ 0.7071067811865476 = 0.9999999999999999.
Understand Sine, cosine and tangent
One idea, three depths
Choose how deeply to explain Sine, cosine and tangent
Calculate sine, cosine and tangent for an angle entered in degrees.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Sine, cosine and tangent to answer this question: calculate sine, cosine and tangent for an angle entered in degrees? Enter Angle in degrees; the calculator shows Sine. For example: At 45°, sine and cosine are √2/2 and tangent is 1. The answer tells you Sine.
Age 15Explain it to a 15-year-oldConnect it to the formula
The unit circle extends right-triangle ratios to angles of any size while preserving their periodic behaviour. The rule is sin θ = opposite/hypotenuse; cos θ = adjacent/hypotenuse; tan θ = sin θ/cos θ. Its input values are Angle in degrees, and the main result is Sine. For example: At 45°, sine and cosine are √2/2 and tangent is 1.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated sine, cosine and tangent relation over the valid real-number domain stated below. The implemented relation is sin θ = opposite/hypotenuse; cos θ = adjacent/hypotenuse; tan θ = sin θ/cos θ, evaluated from Angle in degrees to produce Sine. The unit circle extends right-triangle ratios to angles of any size while preserving their periodic behaviour. Confirm that the input is in degrees; many calculators can instead be set to radians.
Inputs and valid domain
- Angle in degrees must be a finite real number.
Important boundary: Confirm that the input is in degrees; many calculators can instead be set to radians.
The formula
sin θ = opposite/hypotenuse; cos θ = adjacent/hypotenuse; tan θ = sin θ/cos θ
How the calculator works through it
It substitutes Angle in degrees into the formula and exposes every numerical step above. The main output is Sine, accompanied by Cosine, Tangent, Radians.
Read the result correctly
The Sine is the direct answer to “calculate sine, cosine and tangent for an angle entered in degrees.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
At 45°, sine and cosine are √2/2 and tangent is 1.
Where this model stops being reliable
Confirm that the input is in degrees; many calculators can instead be set to radians.
Learn it by changing one value
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Dictionary terms behind this calculator
Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.
These foundations help you understand why Sine, cosine and tangent works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Sine, cosine and tangent uses sin θ = opposite/hypotenuse; cos θ = adjacent/hypotenuse; tan θ = sin θ/cos θ. You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.
Review this foundation about 4 min
Strong support
- Functions, domains and ranges
Domain and range language helps you identify which Sine, cosine and tangent inputs are valid and how the output behaves.
Review this foundation about 6 min
Optional enrichment
- Exponential growth and decay
Exponential models provide a useful extension when Sine, cosine and tangent is applied to multiplicative change.
Review this foundation about 6 min
Mathematics → algorithm → program
Implement this calculation in code
These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.
Algorithm
- Read Angle in degrees.
- Evaluate the principal relationship: sin θ = opposite/hypotenuse; cos θ = adjacent/hypotenuse; tan θ = sin θ/cos θ.
- Return Sine and check the domain conditions described above.
Python
from math import *
def trig_values(value) -> float:
return sin(((value * pi) / 180.0))
assert abs(trig_values(45) - 0.7071067811865475) < 1e-6 * max(1.0, abs(0.7071067811865475))
C
#include <assert.h>
#include <math.h>
double trig_values(double value) {
return sin(((value * 3.141592653589793) / 180.0));
}
int main(void) {
const double expected = 0.7071067811865475;
const double actual = trig_values(45);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double trig_values(double value) {
return std::sin(((value * std::numbers::pi) / 180.0));
}
int main() {
constexpr double expected = 0.7071067811865475;
const double actual = trig_values(45);
assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
Linux x86-64 assembly
x86-64 NASM · System V ABI · Linux · SSE2 with libm where required
; double trig_values(double value)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
extern sin
global trig_values
section .text
trig_values:
push rbp
mov rbp, rsp
sub rsp, 48
movsd [rbp-8], xmm0
mov rax, 0x400921fb54442d18
movq xmm0, rax
movsd [rbp-40], xmm0
movsd xmm0, [rbp-8]
mulsd xmm0, [rbp-40]
movsd [rbp-32], xmm0
mov rax, 0x4066800000000000
movq xmm0, rax
movsd [rbp-48], xmm0
movsd xmm0, [rbp-32]
divsd xmm0, [rbp-48]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
call sin wrt ..plt
movsd [rbp-16], xmm0
movsd xmm0, [rbp-16]
leave
ret
MATLAB
function result = trig_values(value)
result = sin(((value * pi) / 180.0));
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[value_] := Sin[((value * Pi) / 180.0)];
Continue in mathematical software
The downloaded file includes your current inputs and first calculated result. It is created locally.
Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.
Supporting sourcesAcademic referencesPrimary standards, textbooks and complete citations
Standards, reading and academic references
Use the calculator as the worked interaction, then consult the primary standards and academic textbooks listed below. MW SysArc links to the original sources; the explanation on this page is original and does not reproduce them.
Algebra and Trigonometry 2e
Read the related free OpenStax mathematics chaptersCite this book
- APA 7
- Abramson, J. (2021). Algebra and trigonometry 2e. OpenStax. https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites
- MLA 9
- Abramson, Jay. Algebra and Trigonometry 2e. OpenStax, 2021, https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites.
- Chicago author-date
- Abramson, Jay. 2021. Algebra and Trigonometry 2e. Houston, TX: OpenStax. https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites.
OpenStax entries are free to read online. Follow the licence shown on each linked source before redistributing or adapting its content.
Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS
These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.
APA 7
MW SysArc. (2026, July 21). Sine, Cosine and Tangent Calculator. MW SysArc Tools. https://math.mwsysarc.com/precalculus/sine-cosine-tangent-calculator
MLA 9
MW SysArc. “Sine, Cosine and Tangent Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/precalculus/sine-cosine-tangent-calculator. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Sine, Cosine and Tangent Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/precalculus/sine-cosine-tangent-calculator.
Harvard
MW SysArc (2026) ‘Sine, Cosine and Tangent Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/precalculus/sine-cosine-tangent-calculator (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_trig_values_2026,
author = {{MW SysArc}},
title = {Sine, Cosine and Tangent Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/precalculus/sine-cosine-tangent-calculator},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Sine, Cosine and Tangent Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/precalculus/sine-cosine-tangent-calculator
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Sine, cosine and tangent do?
Calculate sine, cosine and tangent for an angle entered in degrees.
How does the Sine, cosine and tangent work?
The calculator applies sin θ = opposite/hypotenuse; cos θ = adjacent/hypotenuse; tan θ = sin θ/cos θ. The unit circle extends right-triangle ratios to angles of any size while preserving their periodic behaviour.
What can I learn from the Sine, cosine and tangent?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed . Calculations tested .