Mathematics · Precalculus

Sine, Cosine and Tangent Calculator

Calculate sine, cosine and tangent for an angle entered in degrees.

Runs locally
Your numbers

Inputs and results stay in this browser. Change one value at a time to explore the relationship.

Your inputCalculatedPassed forward in chains
Sine0.707107
Cosine0.707107
Tangent1
Radians0.785398

Calculation steps

  1. Convert 45° to 0.7853981633974483 radians.
  2. Evaluate sine = 0.7071067811865475 and cosine = 0.7071067811865476.
  3. 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

Learn the missing foundationsI already know these — show the code

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

  1. Read Angle in degrees.
  2. Evaluate the principal relationship: sin θ = opposite/hypotenuse; cos θ = adjacent/hypotenuse; tan θ = sin θ/cos θ.
  3. 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))
          
Current calculator valuesUpdates when you change an input above.
              
            
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)));
}
          
Current calculator valuesUpdates when you change an input above.
              
            
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)));
}
          
Current calculator valuesUpdates when you change an input above.
              
            
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
          
Current calculator valuesUpdates when you change an input above.
              
            
MATLAB
            function result = trig_values(value)
    result = sin(((value * pi) / 180.0));
end
          
Current calculator valuesUpdates when you change an input above.
              
            
Wolfram Language
            ClearAll[mwCalculate];
mwCalculate[value_] := Sin[((value * Pi) / 180.0)];
          
Current calculator valuesUpdates when you change an input above.
              
            

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 chapters
Cite 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 .

MW SysArc Certified