Sin Cos Tan Calculator — Trigonometry Calculator with Steps
Our sin cos tan calculator computes all six trigonometric functions — sine, cosine, tangent, secant, cosecant, and cotangent — for any angle in degrees or radians. It displays exact values for standard angles, shows a step-by-step solution for every calculation, and verifies the Pythagorean identity automatically. Whether you are solving homework, preparing for an exam, or working on an engineering project, this trigonometry calculator gives you reliable, instant results.
Enter an angle, press Calculate All (or just hit Enter), and immediately see sin, cos, and tan together with quadrant analysis, reference angles, reciprocal functions, and inverse trig values. You can also click any common angle — 0°, 30°, 45°, 60°, 90°, and more — to get instant results without typing.
How to Use the Sin Cos Tan Calculator with Steps
Using the calculator is straightforward. Here is how to calculate sin, cos, and tan for any angle:
- Enter your angle in the input field — for example, type
45. - Choose degrees or radians from the dropdown next to the input.
- Click "Calculate All" or press Enter. The calculator computes sin, cos, tan plus all reciprocal and inverse functions.
- Read the step-by-step breakdown — each calculation is explained from angle conversion through the final value, so you can follow exactly how the result was obtained.
You can also click any common angle button (0°, 30°, 45°, 60°, 90°, etc.) to instantly calculate and see exact radical values like √2/2 or √3/2 without manual entry. For focused sine-only analysis, try our specialized sin calculator.
What Does the Sin Cos Tan Calculator Compute?
This calculator with sin cos tan computes far more than the three basic trig functions. Here is everything you get for every angle:
- Sin, Cos, Tan values — computed with adjustable precision (0–12 decimal places), plus exact radical forms for all 17 standard angles.
- Reciprocal functions — secant (sec = 1/cos), cosecant (csc = 1/sin), and cotangent (cot = cos/sin), with proper "undefined" handling at domain boundaries.
- Step-by-step solution — a numbered walkthrough from unit conversion through quadrant identification to final numerical and exact values, ideal for learning or checking homework.
- Quadrant analysis & reference angles — automatically identifies which quadrant the angle falls in and shows the corresponding reference angle.
- Pythagorean identity verification — confirms sin²θ + cos²θ = 1 for your input, and cross-checks tan θ = sin θ / cos θ.
- Inverse trig values — principal values of arcsin, arccos, and arctan in both degrees and radians.
- Degree–radian conversion — every result shows both angular units. For extended angle conversion including DMS format, see our dedicated tool.
Sin Cos Tan Formulas and How They Work
The sin cos tan formulas come from the ratios of a right triangle's sides. The mnemonic SOHCAHTOA encodes all three definitions:
SOH — sin(θ) = Opposite / Hypotenuse
CAH — cos(θ) = Adjacent / Hypotenuse
TOA — tan(θ) = Opposite / Adjacent
On the unit circle, where the radius equals 1, these simplify to: sin(θ) is the y-coordinate of the point where the terminal side meets the circle, cos(θ) is the x-coordinate, and tan(θ) is the slope of the terminal side. This is why sin and cos are always between −1 and 1, while tan can be any real number (and is undefined when cos = 0).
The Pythagorean Identity
The most fundamental trig identity is sin²(θ) + cos²(θ) = 1. It follows directly from the Pythagorean theorem applied to a right triangle with hypotenuse 1. Our calculator verifies this identity for every angle you enter.
How to Find Exact Values of Sin, Cos, and Tan
For the standard angles (0°, 30°, 45°, 60°, 90° and their multiples), trigonometric functions have exact values expressed with square roots. For example, sin(45°) = √2/2, cos(30°) = √3/2, and tan(60°) = √3. Our calculator recognizes all 17 standard angles (0° through 360° in 30°/45° steps) and displays exact radical values alongside the decimal approximation.
The reference table in the calculator above lists every standard angle value — use it as a quick lookup or click any angle to see the full computation with steps.
When Do You Need a Sin Cos Tan Calculator?
Trigonometry Homework and Exams
The step-by-step mode walks you through each calculation the same way your teacher would: convert the angle, identify the quadrant, determine sign, compute the value, and verify with the Pythagorean identity. Use it to check your work or to understand the process when solving trig problems from scratch.
Engineering and Physics Applications
In signal processing, sin and cos define the amplitude and phase of Fourier components. In structural engineering, tan relates vertical and horizontal forces. In robotics, all three functions appear in rotation matrices and forward kinematics. Having a calculator with sin cos tan that computes all functions simultaneously ensures consistency when building transformation matrices or resolving force vectors.
Inverse Trigonometry — Finding Angles from Ratios
If you know a side ratio and need the angle, the inverse sin cos tan calculator section shows arcsin, arccos, and arctan principal values. For example, if sin(θ) = 0.5, the inverse section confirms θ = 30°. For more detailed inverse calculations, our inverse sine calculator handles fractions, DMS output, and general solutions.
Geometry — Right Triangle Problems
Given one angle and one side of a right triangle, sin cos tan lets you find every other measurement. The calculator's exact values are especially useful for special triangles: the 30-60-90 triangle (sides 1 : √3 : 2) and the 45-45-90 triangle (sides 1 : 1 : √2). For complete triangle solving, see our trigonometry calculator which handles all triangle types including oblique triangles with the Law of Sines and Cosines.
About the Author
Marko Šinko
Co-Founder & Lead Developer, AI Math Calculator
Understanding Degrees vs Radians in Trig Calculations
Our calculator supports both degrees and radians. Degrees divide a full rotation into 360 equal parts — intuitive for everyday angles. Radians measure arc length on a unit circle: a full rotation is 2π ≈ 6.283 radians. The conversion formula is:
radians = degrees × π / 180 | degrees = radians × 180 / π
Radians are the standard in calculus, physics, and most programming languages. If you get unexpected results, check your unit setting — this is the #1 source of trig calculation errors. The step-by-step output always shows the conversion so you can verify.
Quadrant Rules — Where Are Sin, Cos, and Tan Positive?
The ASTC rule (All Students Take Calculus) tells you which functions are positive in each quadrant:
- Quadrant I (0°–90°): All positive — sin+, cos+, tan+
- Quadrant II (90°–180°): Only sin+ — cos−, tan−
- Quadrant III (180°–270°): Only tan+ — sin−, cos−
- Quadrant IV (270°–360°): Only cos+ — sin−, tan−
The calculator highlights the active quadrant in the sign reference chart, making it easy to verify whether your result has the correct sign. For cosine-specific analysis, our cos calculator provides extended precision and additional identities.
Why Choose This Sin Cos Tan Calculator?
Unlike basic trig calculators that only return a single decimal value, our sin cos tan calculator gives you the complete picture in one click:
- All 6 trig functions computed simultaneously
- Exact radical values for 17 standard angles
- Full step-by-step solution you can follow
- Adjustable precision from 0 to 12 decimal places
- Quadrant identification with visual sign reference
- Inverse trig values in both degrees and radians
- Pythagorean identity verification for every calculation
- One-click common angles — no typing needed
- Works on mobile and desktop with responsive design
Bookmark this page for instant access to a comprehensive trigonometry calculator for sin, cos, and tan with steps, exact values, and complete quadrant analysis — free, fast, and always accurate.
